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A Joint Deep Learning Approach for Automated Liver and Tumor SegmentationFeb 21 2019Hepatocellular carcinoma (HCC) is the most common type of primary liver cancer in adults, and the most common cause of death of people suffering from cirrhosis. The segmentation of liver lesions in CT images allows assessment of tumor load, treatment ... More
Quotient Problem For Entire Functions with Moving TargetsFeb 21 2019As an analogue of the Hadamard quotient problem in number theory, the quotient problem (in the sense of complex entire functions) for two sequences $F(n)=a_0+a_1f_1^n+\cdots+a_lf_l^n$ and $ G(n)=b_0+b_1g_1^n+\cdots+b_mg_m^n$, has been solved, where the ... More
Quasi-trees and geodesic treesFeb 20 2019A quasi-tree is a metric tree that is doubling and of bounded turning. We prove that every quasi-tree can be mapped to a geodesic tree by a quasisymmetric homeomorphism. We also show that every quasi-tree has conformal dimension equal to $1$.
A Note on Compactness and Singular Points of Composition Operators on Domains in $\mathbb{C}^n$Feb 20 2019Let $\Omega\subset \mathbb{C}^n$ for $n\geq 2$ be a bounded pseudoconvex domain with a $C^1$-smooth boundary. We study the boundedness of composition operators on the $p$-Bergman spaces of $\Omega$ for $p\in [1,\infty)$. We also study the compactness ... More
Dynamic Cell Imaging in PET with Optimal Transport RegularizationFeb 20 2019We propose a novel dynamic image reconstruction method from PET listmode data that could be particularly suited to tracking single or small numbers of cells. In contrast to conventional PET reconstruction the proposed method combines the information from ... More
Row contractions annihilated by interpolating vanishing idealsFeb 18 2019We study similarity classes of commuting row contractions annihilated by what we call higher order vanishing ideals of interpolating sequences. Our main result exhibits a Jordan-type direct sum decomposition for these row contractions. We illustrate how ... More
A four dimensional Jensen formulaFeb 18 2019We prove a Jensen formula for slice-regular functions of one quaternionic variable. The formula relates the value of the function and of its first two derivatives at a point with its integral mean on a three dimensional sphere centred at that point and ... More
On the slit motion obeying chordal Komatu-Loewner equation with finite explosion timeFeb 18 2019This paper studies the behavior of solutions near the explosion time to the chordal Komatu-Loewner equation for slits, motivated by the preceding studies by Bauer and Friedrich (2008) and by Chen and Fukushima (2018). The solution to this equation represents ... More
Functions of noncommuting operators under perturbation of class $\boldsymbol{S}_p$Feb 17 2019In this article we prove that for $p>2$, there exist pairs of self-adjoint operators $(A_1,B_1)$ and $(A_2,B_2)$ and a function $f$ on the real line in the homogeneous Besov class $B_{\infty,1}^1({\Bbb R}^2)$ such that the differences $A_2-A_1$ and $B_2-B_1$ ... More
Coefficient bounds for close-to-convex functions associated with vertical strip domainFeb 17 2019By considering a certain univalent function in the open unit disk U, that maps U onto a strip domain, we introduce a new class of analytic and close-to-convex functions by means of a certain non-homogeneous Cauchy-Euler-type differential equation. We ... More
The isometries of the space of Kähler metricsFeb 16 2019Given a compact K\"ahler manifold, we prove that all global isometries of the space of K\"ahler metrics are induced by biholomorphisms and anti-biholomorphisms of the manifold. In particular, there exist no global symmetries for Mabuchi's metric. Moreover, ... More
One-box conditions for Carleson measures for the Dirichlet spaceFeb 15 2019We give a simple proof of the fact that a finite measure $\mu$ on the unit disk is a Carleson measure for the Dirichlet space if it satisfies the Carleson one-box condition $\mu(S(I))=O(\phi(|I|))$, where $\phi:(0,2\pi]\to(0,\infty)$ is an increasing ... More
Outer functions and divergence in de Branges-Rovnyak spacesFeb 15 2019In most classical holomorphic function spaces on the unit disk in which the polynomials are dense, a function $f$ can be approximated in norm by its dilates $f_r(z):=f(rz)~(r<1)$, in other words, $\lim_{r\to1^-}\|f_r-f\|=0$. We construct a de Branges-Rovnyak ... More
Linear maps preserving inner functionsFeb 15 2019We show that, for many holomorphic function spaces on the unit disk, a continuous endomorphism that sends inner functions to inner functions is necessarily a weighted composition operator.
Topology of Gleason Parts in maximal ideal spaces with no analytic discsFeb 14 2019We strengthen, in various directions, the theorem of Garnett that every sigma-compact, completely regular space X occurs as a Gleason part for some uniform algebra. In particular, we show that the uniform algebra can always be chosen so that its maximal ... More
Topology of Gleason Parts in maximal ideal spaces with no analytic discsFeb 14 2019Feb 15 2019We strengthen, in various directions, the theorem of Garnett that every $\sigma$-compact, completely regular space $X$ occurs as a Gleason part for some uniform algebra. In particular, we show that the uniform algebra can always be chosen so that its ... More
Monge-Ampère of Pac-ManFeb 13 2019We show that the Monge-Amp\`ere density of the extremal function $V_P$ for a non-convex Pac-Man set $P\subset {\bf R}^2$ tends to a finite limit as we approach the vertex $p$ of $P$ linearly but with a value that may vary with the line. On the other hand, ... More
On the number of zeros of functions in analytic quasianalytic classesFeb 13 2019A space of analytic functions in the unit disc with uniformly continuous derivatives is said to be quasianalytic if the boundary value of a non-zero function from the class can not have a zero of infinite multiplicity. Such classes were described in the ... More
On factorization of p-adic meromorphic functionsFeb 13 2019In this paper, we study primeness and pseudo primeness of p-adic meromorphic functions. We also consider left (resp. right ) primeness of these functions. We give, in particular, sufficient conditions for a meromorphic function to satisfy such properties. ... More
Elliptic extension of Gustafson's $q$-integral of type $G_2$Feb 13 2019The evaluation formula for an elliptic beta integral of type $G_2$ is proved. The integral is expressed by a product of Ruijsenaars' elliptic gamma functions, and the formula includes that of Gustafson's $q$-beta integral of type $G_2$ as a special limiting ... More
Second main theorems with weighted counting functions and its applicationsFeb 12 2019The purpose of this article has two fold. The first is to generalize some recent second main theorems for the mappings and moving hyperplanes of $\P^n(\C)$ to the case where the counting functions are truncated multiplicity (by level $n$) and have different ... More
The double point formula with isolated singularities and canonical embeddingsFeb 12 2019Motivated by the embedding problem of canonical models in small codimension, we extend Severi's double point formula to the case of surfaces with rational double points, and we give more general double point formulae for varieties with isolated singularities. ... More
Identifying logarithmic tractsFeb 12 2019We show that a direct tract bounded by a simple curve is a logarithmic tract and further give sufficient conditions for a direct tract to contain logarithmic tracts. As an application of these results, an example of a function with infinitely many direct ... More
Lemniscate Convexity and Other Properties of Generalized Bessel FunctionsFeb 12 2019Sufficient conditions on associated parameters $p,b$ and $c$ are obtained so that the generalized and \textquotedblleft{normalized}\textquotedblright{} Bessel function $u_p(z)=u_{p,b,c}(z)$ satisfies $|(1+(zu''_p(z)/u'_p(z)))^2-1|<1$ or $|((zu_p(z))'/u_p(z))^2-1|<1$. ... More
Carleson measures on simply connected domainsFeb 12 2019We study the Carleson measures associated to the Hardy and weighted Bergman spaces defined on general simply connected domains. This program was initiated by Zinsmeister in his paper \textit{Les domaines de Carleson }(1989), where he shows that the geometry ... More
How to count the number of zeros that a polynomial has on the unit circle?Feb 12 2019The classical problem of counting the number of real zeros of a real polynomial was solved a long time ago by Sturm. The analogous problem of counting the number of zeros that a polynomial has on the unit circle is, however, still an open problem. In ... More
Lipschitz property of minimisers between double connected surfacesFeb 11 2019We study the global Lipschitz character of minimisers of the Dirichlet energy of diffeomorphisms between doubly connected domains with smooth boundaries from Riemann surfaces. The key point of the proof is the fact that minimisers are certain Noether ... More
Moving Seshadri Constants, and Coverings of Varieties of Maximal Albanese DimensionFeb 11 2019Feb 18 2019Let $X$ be a smooth projective complex variety of maximal Albanese dimension, and let $L \to X$ be a big line bundle. We prove that the moving Seshadri constants of the pull-backs of $L$ to suitable finite abelian \'etale covers of $X$ are arbitrarily ... More
Moving Seshadri Constants, and Coverings of Varieties of Maximal Albanese DimensionFeb 11 2019Let $X$ be a smooth projective complex variety of maximal Albanese dimension, and let $L \to X$ be a big line bundle. We prove that the moving Seshadri constants of the pull-backs of $L$ to suitable finite abelian \'etale covers of $X$ are arbitrarily ... More
Doubly periodic monopoles and $q$-difference modulesFeb 10 2019An interesting theme in complex differential geometry is to find a correspondence between algebraic objects and differential geometric objects. One of the most attractive is the non-abelian Hodge theory of Simpson. In this paper, pursuing an analogue ... More
Trajectories of semigroups of holomorphic functions and harmonic measureFeb 09 2019We give an explicit relation between the slope of the trajectory of a semigroup of holomorphic functions and the harmonic measure of the associated planar domain ${\varOmega}$. We use this to construct a semigroup whose slope is an arbitrary interval ... More
On the multipliers at fixed points of self-maps of the projective planeFeb 09 2019This paper deals with holomorphic self-maps of the complex projective plane and the algebraic relations among the eigenvalues of the derivatives at the fixed points. These eigenvalues are constrained by certain index theorems such as the holomorphic Lefschetz ... More
On the multipliers at fixed points of self-maps of the projective planeFeb 09 2019Feb 15 2019This paper deals with holomorphic self-maps of the complex projective plane and the algebraic relations among the eigenvalues of the derivatives at the fixed points. These eigenvalues are constrained by certain index theorems such as the holomorphic Lefschetz ... More
On Poletsky type inequality for mappings of Riemannian surfacesFeb 09 2019In this paper, we obtain upper estimates for the distortion of the modulus of families of paths under mappings of the Sobolev class, whose dilatation is locally integrable. As a consequence, theorems on the local and boundary behavior of the indicated ... More
Characterization of polynomials whose large powers have fully positive coefficientsFeb 09 2019We give a criterion which characterizes a real multi-variate Laurent polynomial with full-dimensional smooth Newton polytope to have the property that all sufficiently large powers of the polynomial have fully positive coefficients. Here a Laurent polynomial ... More
$(g,k)$-Fermat curvesFeb 08 2019Let $G$ be a co-compact torsion free Fuchsian group of genus $g \geq2$ and, for each integer $k \geq 2$, $G_{k}$ be its normal subgroup generated by the $k$-powers of the elements of $G$ together its commutators. There is a natural holomorphic embedding ... More
Solutions of the $\bar \partial $-equation on Kähler manifold with compact supportFeb 07 2019We study the $\bar \partial $-equation in complete K\"ahler manifolds. The aim is to get $L^{r}$ and Sobolev estimates on solutions with compact support. We prove and use estimates on solutions on Poisson equation with compact support and the link with ... More
An analytic approach to the Riemann hypothesisFeb 07 2019In this work we consider a new functional equation for the Riemann zeta-function in the critical half-strip. With the help of this equation we prove that finding non-trivial zeros of the Riemann zeta-function outside the critical line would be equivalent ... More
Separation of variables in the semistable rangeFeb 07 2019In this paper, we give an alternative proof of separation of variables for scalar-valued polynomials $P:(\mathbb R^m)^k\to\mathbb C$ in the semistable range $m\geq 2k-1$ for the symmetry given by the orthogonal group $O(m)$. It turns out that uniqueness ... More
Starlikeness Associated With The Exponential FunctionFeb 07 2019Given a domain $\Omega$ in the complex plane $\mathbb{C}$ and a univalent function $q$ defined in an open unit disk $\mathbb{D}$ with nice boundary behaviour, Miller and Mocanu studied the class of admissible functions $\Psi(\Omega,q)$ so that the differential ... More
Self-intersections of Laurent polynomials and the density of Jordan curvesFeb 07 2019We extend Quine's bound on the number of self-intersection of curves with polynomial parameterization to the case of Laurent polynomials. As an application, we show that circle embeddings are dense among all maps from a circle to a plane with respect ... More
On a problem of PichoridesFeb 06 2019Let $S^{(\Lambda)}$ denote the classical Littlewood-Paley square function formed with respect to a lacunary sequence $\Lambda$ of positive integers. Motivated by a remark of Pichorides, we obtain sharp asymptotic estimates of the behaviour of the operator ... More
A classical functional generalization of the first Barnes lemmaFeb 06 2019We give a brief account and a simpler proof of a contour integral formula for the Gauss hypergeometric function. Such formula is alternative to Barnes's integral formula and generalizes the first Barnes Lemma.
LCK metrics on toric LCS manifoldsFeb 06 2019We show a bijective correspondence between compact toric locally conformally symplectic manifolds which admit a compatible complex structure and pairs $(C,a)$, where $C$ is a good cone in the dual Lie algebra of the torus and $a$ is a positive real number. ... More
Schur parameters and Carathéodory classFeb 06 2019The Schur (resp. Carath\'eodory) class consists of all the analytic functions $f$ on the unit disk with $|f|\le 1$ (resp. $\Re f>0$ and $f(0)=1$). The Schur parameters $\gamma_0,\gamma_1,\dots (|\gamma_j|\le 1)$ are known to parametrize the coefficients ... More
Geometric pluripotential theory on Kähler manifoldsFeb 06 2019Finite energy pluripotential theory accommodates the variational theory of equations of complex Monge-Amp\`ere type arising in K\"ahler geometry. Recently it has been discovered that many of the potential spaces involved have a rich metric geometry, effectively ... More
Integral means inequalities, convolution, and univalent functionsFeb 05 2019We use the Baernstein star-function to investigate several questions about the integral means of the convolution of two analytic functions in the unit disc. The theory of univalent functions plays a basic role in our work.
Cyclic Symmetry on Complex Tori and Bagnera-De Franchis ManifoldsFeb 05 2019We describe the possible linear actions of a cyclic group $G = \mathbb{Z} /n$ on a complex torus, using the cyclotomic exact sequence for the group algebra $\mathbb{Z} [G]$. The main application is devoted to a structure theorem for Bagnera-De Franchis ... More
Siciak's homogeneous extremal functions, holomorphic extension and a generalization of Helgason's support theoremFeb 04 2019We prove that a function, which is defined on a union of lines $\mathbb{C} E$ through the origin in $\mathbb{C}^n$ with direction vectors in $E\subset \mathbb{C}^n$ and is holomorphic of fixed finite order and finite type along each line, extends to an ... More
Solvability in Gevrey classes of some linear functional equationsFeb 03 2019In this paper, we associate to each positive number k a new class of endomorphisms of the sheaf of germs of holomorphic functions on [-1,1] and prove the solvability in the Gevrey class G_k([-1,1]) of some linear functional equations related to endomorphisms. ... More
Notes on the Szego minimum problem. I. Measures with deep zeroesFeb 03 2019The classical Szego polynomial approximation theorem states that the polynomials are dense in the space $L^2(\rho)$, where $\rho$ is a measure on the unit circle, if and only if the logarithmic integral of the measure $\rho$ diverges. In this note we ... More
Notes on the Szego minimum problem. II. Singular measuresFeb 03 2019In this part, we prove several quantitative results concerning with the Szego minimum problem for classes of measure on the unit circle concentrated on small subsets. As a by-product, we refute one conjecture of Nevai. This note can be read independently ... More
Hodge cycles for cubic hypersurfacesFeb 03 2019We study an algebraic cycle of the form $Z_0= r {\mathbb P}^{\frac{n}{2}}+\check r \check{\mathbb P}^{\frac{n}{2}}$, $r \in{\mathbb N},\check r \in{\mathbb Z},\ \ 1\leq r , |\check r |\leq 10,\ \ \gcd ( r ,\check r )=1$, inside the cubic Fermat variety ... More
About a conjecture on difference equations in quasianalytic Carleman classesFeb 02 2019In this paper we obtain a partial answer to a conjecture on the solvabilty of linear difference equations in quasianalytic Carleman classes.
A Conjecture of TrautmanFeb 01 2019In 1998 the physicist Andre Trautman conjectured that a three-dimensional CR manifold is locally realizable if and only if its canonical bundle admits a closed nowhere zero section. We review the relevant definitions, give the physical context, and outline ... More
Study of some holomorphic curves in $\C^3$ and their projection into the complex projectve space $\C P^2$Jan 31 2019We study holomorphic curves $f:\C\longrightarrow \C^3$ avoiding four complex hyperplanes and a real subspace of real dimension four or five in $\C^3$. We show that the projection of $f$ into the complex projective space $\C P^2$ is not necessarily constant. ... More
Algebraic surfaces with infinitely many twistor linesJan 31 2019Feb 04 2019We prove that a reduced and irreducible algebraic surface in $\mathbb{CP}^{3}$ containing infinitely many twistor lines cannot have odd degree. Then, exploiting the theory of quaternionic slice regularity and the normalization map of a surface, we give ... More
Meromorphic limits of automorphismsJan 30 2019Let $X$ be a compact complex manifold in the Fujiki class $\mathscr{C}$. We study the compactification of $\operatorname{Aut}^0(X)$ given by its closure in Barlet cycle space. The boundary points give rise to non-dominant meromorphic self-maps of $X$. ... More
Factorization by elementary matrices, null-homotopy and products of exponentials for invertible matrices over ringsJan 30 2019Feb 11 2019Let $R$ be a commutative unital ring. A well-known factorization problem is whether any matrix in $\mathrm{SL}_n(R)$ is a product of elementary matrices with entries in $R$. To solve the problem, we use two approaches based on the notion of the Bass stable ... More
Syzygies of A Tower of Compact Local Hermitian Symmetric Spaces of Finite TypeJan 30 2019Let $X$ be a $n$ dimensional compact local Hermitian symmetric space of non-compact type and $L=\shO(K_X)\tens\shO(qM)$ be an adjoint line bundle. Let $c>0$ be a constant. Assume the curvature of $M$ is $\ge c\omega$, where $\omega$ is the k\"ahler form ... More
Deformation limit of Moishezon manifoldsJan 30 2019Let $\pi: \mathcal{X}\rightarrow \Delta$ be a holomorphic family of compact complex manifolds over an open disk in $\mathbb{C}$. If the fiber $X_t:=\pi^{-1}(t)$ for each nonzero $t$ in an uncountable subset $B$ of $\Delta$ is Moishezon and the reference ... More
On modifications of the exponential integral with the Mittag-Leffler functionJan 29 2019In this paper we survey the properties of the Schelkunoff modification of the Exponential integral and we generalize it with the Mittag-Leffler function. So doing we get a new special function (as far as we know) that may be relevant in linear viscoelasticity ... More
Boundary integral formula for harmonic functions on Riemann surfacesJan 28 2019We construct a boundary integral formula for harmonic functions on open, smoothly-bordered subdomains of Riemann surfaces embeddable into $\C\P^2$. The formula may be considered as an analogue of the Green's formula for domains in $\C$.
CURE: Curvature Regularization For Missing Data RecoveryJan 28 2019Missing data recovery is an important and yet challenging problem in imaging and data science. Successful models often adopt certain carefully chosen regularization. Recently, the low dimension manifold model (LDMM) was introduced by S.Osher et al. and ... More
On a trace formula for functions of noncommuting operatorsJan 28 2019The main result of the paper is that the Lifshits--Krein trace formula cannot be generalized to the case of functions of noncommuting self-adjoint operators. To prove this, we show that for pairs $(A_1,B_1)$ and $(A_2,B_2)$ of bounded self-adjoint operators ... More
Zeros of Normalized Sections of Non Convergent Power SeriesJan 25 2019A well known result due to Carlson affirms that a power series with finite and positive radius of convergence R has no Ostrowski gaps if and only if the sequence of zeros of its nth sections is asymptotically equidistributed to {|z|=R}. Here we extend ... More
Geometric flow, Multiplier ideal sheaves and Optimal destabilizer for a Fano manifoldJan 24 2019S. K. Donaldson asked whether the lower bound of the Calabi functional is achieved by a sequence the normalized Donaldson-Futaki invariants. We answer the question for the Ricci curvature formalism, in place of the scalar curvature. The principle is that ... More
On a generalization of the Gaussian plane to three dimensionsJan 24 2019Each associative division algebra over the real number field of finite dimension $n \in \mathbb{N}$ is isomorphic (1) to $\mathbb{R}$ (the field of all real numbers, $n=1$), or, (2) to $\mathbb{C}$ (the field of all Gaussian complex numbers, $n=2$), or, ... More
Linear invariants of complex manifolds and their plurisubharmonic variationsJan 24 2019For a bounded domain $D$ and a real number $p>0$, we denote by $A^p(D)$ the space of $L^p$ integrable holomorphic functions on $D$, equipped with the $L^p$- pseudonorm. We prove that two bounded hyperconvex domains $D_1\subset \mc^n$ and $D_2\subset \mc^m$ ... More
Sharp Complex Convexity EstimatesJan 23 2019In this paper we determine the value of the best constants in the 2-uniform PL-convexity estimates of $\mathbb C$. This solves a problem posed by W. J. Davis, D. J. H. Garling and N. Tomczak-Jaegermann.
Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scaleJan 23 2019We give sufficient conditions for quasiconformal mappings between simply connected Lipschitz domains to have H\"older, Sobolev and Triebel-Lizorkin regularity in terms of the regularity of the boundary of the domains and the regularity of the Beltrami ... More
A necessary and sufficient condition for global convergence of the complex zeros of random orthogonal polynomialsJan 22 2019Consider random polynomials of the form $G_n = \sum_{i=0}^n \xi_i p_i$, where the $\xi_i$ are i.i.d. non-degenerate complex random variables, and $\{p_i\}$ is a sequence of orthonormal polynomials with respect to a regular measure $\tau$ supported on ... More
Semi-isometric CR immersions of CR manifolds into Kähler manifolds and applicationsJan 22 2019We study the geometry of the second fundamental form of the semi-isometric CR immersions from strictly pseudoconvex CR manifolds into K\"ahler manifolds in connection with several problems in complex variables. This study is applied in particular to estimate ... More
The equivalence principle for almost periodic functionsJan 22 2019Given two arbitrary almost periodic functions, we prove that the existence of a common open vertical strip $V$, where both functions assume the same set of values on every open vertical substrip included in $V$, is a necessary and sufficient condition ... More
A transcendental Hénon map with an oscillating wandering Short $\mathbb{C}^2$Jan 22 2019Short $\mathbb{C}^2$'s were constructed in [F] as attracting basins of a sequence of holomorphic automorphisms whose rate of attraction increases superexponentially. The goal of this paper is to show that such domains also arise naturally as autonomous ... More
Extremal problems for polynomials with real rootsJan 22 2019We consider polynomials of degree $d$ with only real roots and a fixed value of discriminant, and study the problem of minimizing the absolute value of polynomials at a fixed point off the real line. There are two types of polynomials that turn out to ... More
Maximum Principles for Matrix-Valued Analytic FunctionsJan 22 2019To what extent is the maximum modulus principle for scalar-valued analytic functions valid for matrix-valued analytic functions? In response, we discuss some maximum norm principles for such functions that do not appear to be widely known, deduce maximum ... More
Besov spaces induced by doubling weightsJan 21 2019Let $1\le p<\infty$, $0<q<\infty$ and $\nu$ be a two-sided doubling weight satisfying $$\sup_{0\le r<1}\frac{(1-r)^q}{\int_r^1\nu(t)\,dt}\int_0^r\frac{\nu(s)}{(1-s)^q}\,ds<\infty.$$ The weighted Besov space $\mathcal{B}_{\nu}^{p,q}$ consists of those ... More
On sharp lower bounds for Calabi type functionals and destabilizing properties of gradient flowsJan 19 2019Let $X$ be a compact K\"ahler manifold with a given ample line bundle $L$. In \cite{Don05}, Donaldson proved that the Calabi energy of a K\"ahler metric in $c_1(L)$ is bounded from below by the supremum of a normalized version of the minus Donaldson--Futaki ... More
$l^p-l^q$ estimates of Bergman projector on the minimal ballJan 18 2019We study the $L^p-L^q$ boundedness of Bergman projector on the minimal ball. This improves an important result of \cite{MY} due to G. Mengotti and E. H. Youssfi.
On Hölder continuity of mappings in domains and on boundariesJan 18 2019We study mappings with branching of a domain of Euclidean space. The H\"older and Lipschitz continuity are established for one class of spatial mappings whose characteristic satisfies the Dini type condition in a given domain. In addition, we found conditions ... More
Eigenvalues of the Kohn Laplacian and deformations of pseudohermitian structures on compact embedded strictly pseudoconvex CR manifoldsJan 17 2019We study the eigenvalues of the Kohn Laplacian on a closed embedded strictly pseudoconvex CR manifold as functionals on the set of positive oriented contact forms $\mathcal{P}_+$. We show that the functionals are continuous with respect to a natural topology ... More
Isoperimetric inequalities for Bergman analytic contentJan 17 2019The Bergman $p$-analytic content ($1\leq p<\infty $) of a planar domain $\Omega $ measures the $L^{p}(\Omega )$-distance between $\overline{z}$ and the Bergman space $A^{p}(\Omega )$ of holomorphic functions. It has a natural analogue in all dimensions ... More
Symmetries of Transversely Projective FoliationsJan 17 2019Given a (singular, codimension 1) holomorphic foliation F on a complex projective manifold X, we study the group PsAut(X, F) of pseudo-automorphisms of X which preserve F ; more precisely, we seek sufficient conditions for a finite index subgroup of PsAut(X, ... More
Quasisymmetric embeddings of slit Sierpiński carpetsJan 17 2019In this paper we study the problem of quasisymmetrically embedding metric carpets, i.e., spaces homeomorphic to the classical Sierpi\'nski carpet, into the plane. We provide a complete characterization in the case of so-called dyadic slit carpets. The ... More
Spiders' webs in the punctured planeJan 16 2019Many authors have studied sets, associated with the dynamics of a transcendental entire function, which have the topological property of being a spider's web. In this paper we adapt the definition of a spider's web to the punctured plane. We give several ... More
A Newton method for harmonic mappings in the planeJan 16 2019We present an iterative root finding method for harmonic mappings in the complex plane, which is a generalization of Newton's method for analytic functions. The complex formulation of the method allows an analysis in a complex variables spirit. For zeros ... More
On singularly perturbed linear initial value problems with mixed irregular and Fuchsian time singularitiesJan 16 2019We consider a family of linear singularly perturbed PDE relying on a complex perturbation parameter $\epsilon$. As in a former study of the authors (A. Lastra, S. Malek, Parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems, J. ... More
Algorithms for $\ell_p$-based semi-supervised learning on graphsJan 15 2019We develop fast algorithms for solving the variational and game-theoretic $p$-Laplace equations on weighted graphs for $p>2$. The graph $p$-Laplacian for $p>2$ has been proposed recently as a replacement for the standard ($p=2$) graph Laplacian in semi-supervised ... More
Equilibrium measures of meromorphic self-maps on non-Kahler manifoldsJan 15 2019Let $X$ be a compact complex non-K\"ahler manifold and $f$ a dominant meromorphic self-map of $X$. Examples of such maps are self-maps of Hopf manifolds, Calabi-Eckmann manifolds, non-tori nilmanifolds and their blowups. We prove that if $f$ has a dominant ... More
Quadratization in discrete optimization and quantum mechanicsJan 14 2019A book about turning high-degree optimization problems into quadratic optimization problems that maintain the same global minimum (ground state). This book explores quadratizations for pseudo-Boolean optimization, perturbative gadgets used in QMA completeness ... More
The closed range property for the $\overline{\partial}$-operator on planar domainsJan 14 2019Let $\Omega\subset\mathbb{C}$ be an open set. We show that $\overline{\partial}$ has closed range in $L^{2}(\Omega)$ if and only if the Poincar\'e-Dirichlet inequality holds. Moreover, we give necessary and sufficient potential-theoretic conditions for ... More
Remarks on Chern-Einstein Hermitian metricsJan 14 2019We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.
A characterization of real holomorphic chains and applications in the study of algebraic cyclesJan 14 2019We show that a current $T$ on an open set $U\subset \C^n$ is a real holomorphic $k$-chain if and only if $T$ is locally real rectifiable, closed and has $\mathcal{H}^{2k}$-locally finite support. This result is applied to get some results about homology ... More
Adiabatic Limit and Deformations of Complex StructuresJan 13 2019Based on our recent adaptation of the adiabatic limit construction to the case of complex structures, we give a new proof of the fact, that we first proved in 2009 and 2010, that the deformation limiting manifold of any holomorphic family of Moishezon ... More
Existence of the rhombohedral and tetragonal deformation families of the gyroidJan 13 2019We provide an existence proof for two 1-parameter families of triply periodic minimal surfaces of genus three, namely the tG family with tetragonal symmetry that contains the gyroid, and the rGL family with rhombohedral symmetry that contains the gyroid ... More
Inclusion properties for bi-univalent functions of complex order defined by combining of Faber polynomial expansions and Fibonacci numbersJan 13 2019In this present investigation, we introduce the new class R of bi-univalent functions defined by using the Tremblay fractional derivative operator. Additionally, we use the Faber polynomial expansions and Fibonacci numbers to derive bounds for the general ... More
Fréchet-valued formal power seriesJan 12 2019Let $A$ be a non-projectively-pluripolar set in a Fr\'{e}chet space $E.$ We give sufficient conditions to ensure the convergence on some zero-neighbourhood in $E$ of a (sequence of) formal power series of Fr\'{e}chet-valued continuous homogeneous polynomials ... More
Radii of starlikeness and convexity of generalized Mittag-Leffler functionsJan 11 2019In this paper our aim is to find the radii of starlikeness and convexity of the generalized Mittag-Leffler function for three different kinds of normalization by using their Hadamard factorization in such a way that the resulting functions are analytic ... More
Local holomorphic mappings respecting homogeneous subspaces on rational homogeneous spacesJan 11 2019Let $G/P$ be a rational homogeneous space (not necessarily irreducible) and $x_0\in G/P$ be the point at which the isotropy group is $P$. The $G$-translates of the orbit $Qx_0$ of a parabolic subgroup $Q\subsetneq G$ such that $P\cap Q$ is parabolic are ... More