Latest in math.dg

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Constant mean curvature n-noids in hyperbolic spaceMay 22 2019Using the DPW method, we construct genus zero Alexandrov-embedded constant mean curvature (greater than one) surfaces with any number of Delaunay ends in hyperbolic space.
Twisted differential KO-theoryMay 22 2019We provide a systematic approach to twisting differential KO-theory leading to a construction of the corresponding twisted differential Atiyah-Hirzebruch spectral sequence (AHSS). We relate and contrast the degree two and the degree one twists, whose ... More
On Complete Conformally flat submanifolds with nullity in Euclidean spaceMay 22 2019In this note, we investigate conformally flat submanifolds of Euclidean space with positive index of relative nullity. Let $M^n$ be a complete conformally flat manifold and let $f\colon M^n\to \R^m$ be an isometric immersion. We prove the following results: ... More
Riemannian properties of Engel structuresMay 22 2019This paper is about geometric and Riemannian properties of Engel structures, i.e. maximally non-integrable $2$-plane fields on $4$-manifolds. Two $1$-forms $\alpha$ and $\beta$ are called Engel defining forms if $\mathcal{D}=\ker\alpha\cap\ker\beta$ is ... More
Biharmonic Hermitian vector bundles over compact Kaehlar Einstein manifoldsMay 22 2019In this paper, we show that, for every Hermitian vector bundle over a compact Kaehler Einstein manifold, if the projection is biharmonic, then it is harmonic.
A Cauchy problem for minimal spacelike surfaces in $\mathbb{R}^4_2$May 21 2019We give a definition of isoclinic parametric surfaces in $\mathbb{R}^4_2$ and prove that such an isoclinic conformal immersion comes from two holomorphic functions. A Cauchy problem was proposed and solved, namely: construct an isoclinic and minimal positive ... More
Dirichlet boundary values on Euclidean balls with infinitely many solutions for the minimal surface systemMay 21 2019We make systematic developments on Lawson-Osserman constructions relating to the Dirichlet problem (over unit disks) for minimal surfaces of high codimension in their 1977 Acta paper. In particular, we show the existence of boundary functions for which ... More
Band width estimates via the Dirac operatorMay 21 2019Let $M$ be a closed connected spin manifold such that its spinor Dirac operator has non-vanishing (Rosenberg) index. We prove that for any Riemannian metric on $V = M \times [-1,1]$ with scalar curvature bounded below by $\sigma > 0$, the distance between ... More
The Lie symmetry group of the general Lienard-type equationMay 21 2019We consider the general Lienard-type equation $\ddot{u} = \sum_{k=0}^n f_k \dot{u}^k$ for $n\geq 4$. This equation naturally admits the Lie symmetry $\frac{\partial}{\partial t}$. We completely characterize when this equation admits another Lie symmetry, ... More
On the CR analogue of Frankel conjecture and a smooth representative of the first Kohn-Rossi cohomology groupMay 21 2019In this note, we affirm the partial answer to the Frankel conjecture in a closed, spherical, strictly pseudoconvex CR manifold with positive constant Tanaka-Webster scalar curvature. More precisely, we give a criterion of pseudo-Einstein contact forms ... More
Harmonic surfaces in the Cayley planeMay 20 2019We consider the twistor theory of nilconformal harmonic maps from a Riemann surface into the Cayley plane $\mathbf{O} P^2=F_4/\mathrm{Spin}(9)$. By exhibiting this symmetric space as a submanifold of the Grassmannian of $10$-dimensional subspaces of the ... More
Some properties of geodesic $(α,E)$-preinvex functions on a Riemannian manifoldMay 20 2019In this article, we have introduced the concept of \textit{geodesic $(\alpha,E)$-invex set} and by using this concept the notion of \textit{geodesic $(\alpha,E)$-preinvex functions} and \textit{geodesic $(\alpha,E)$-invex functions} are developed on a ... More
The correspondence formula of Dolbeault complex on pair deformationMay 20 2019Given a holomorphic family of pairs $\{(X_t,E_t)\}$, where each $E_t$ is holomorphic vector bundle over compact complex manifold $X_t$. For small enough $t$, we get a correspondence between the Dolbeault complex of $E_t$-valued $(p,q)$-forms on $X_t$ ... More
Lectures on curvature flow of networksMay 19 2019We present a collection of results on the evolution by curvature of networks of planar curves. We discuss in particular the existence of a solution and the analysis of singularities.
The Partial Ricci Flow on $\mathfrak{g}$-foliationsMay 19 2019We introduce and study new structures, which generalize the 3-(quasi-)Sasakian structure, an $f$-{structure with parallelizable kernel}, and an {almost para-$\phi$-structure with complemented frames} (having constant partial Ricci curvature) and are of ... More
The uniform perfectness of diffeomorphism groups of open manifoldsMay 19 2019In this paper we study the uniform perfectness, boundedness and uniform simplicity of diffeomorphism groups of compact manifolds with boundary and open manifolds and obtain some upper bounds of their diameters with respect to commutator length, those ... More
Escobar constants of planar domainsMay 18 2019We initiate the study of the higher order Escobar constants $I_k(M)$, $k\geq 3$, on bounded planar domains $M$. For a domain $M$ in $\mathbb{R}^2$ with Lipschitz and piecewise smooth boundary, we conjecture that its $k$-th Escobar constant $I_k(M)$ is ... More
A contact geometry framework for field theories with dissipationMay 17 2019We develop a new geometric framework suitable for the treatment of field theories with dissipation. To this end we define the notion of $k$-contact structure. With it, we introduce the so-called $k$-contact Hamiltonian systems, which are a generalization ... More
Diameters of Ball IntersectionsMay 17 2019We prove the diameter of the intersection of two closed convex balls in a Riemannian manifold eventually decreases continuously as the centers of the balls move apart.
$W^{s,\frac{n}{s}}$-maps with positive distributional JacobiansMay 17 2019We extend the well-known result that any $f \in W^{1,n}(\Omega,\mathbb{R}^n)$, $\Omega \subset \mathbb{R}^n$ with strictly positive Jacobian is actually continuous: it is also true for fractional Sobolev spaces $W^{s,\frac{n}{s}}(\Omega)$ for any $s \geq ... More
LcK structures with holomorphic Lee vector field on Vaisman-type manifoldsMay 17 2019We give a complete description of all locally conformally K\"ahler structures with holomorphic Lee vector field on a compact complex manifold of Vaisman type. This provides in particular examples of such structures whose Lee vector field is not homothetic ... More
Minimizing geodesic nets and critical points of distanceMay 17 2019In this paper we establish a relationship between geodesic nets and critical points of the distance function. We bound the number of balanced points for certain minimizing geodesic nets on manifolds homeomorphic to the $n$-sphere. We also bound the length ... More
Reconstruction of a Riemannian manifold from noisy intrinsic distancesMay 17 2019We consider reconstruction of a manifold, or, invariant manifold learning, where a smooth Riemannian manifold $M$ is determined from intrinsic distances (that is, geodesic distances) of points in a discrete subset of $M$. In the studied problem the Riemannian ... More
Existence of infinitely many minimal hypersurfaces in low dimensions, after F.C. Marques, A.A. Neves et A. Song (Bourbaki Seminar)May 17 2019A classical result by Marston Morse asserts that on some ellipsoids of ${\mathbb R}^3$ there exists exactly 3 closed and simple geodesics. The goal of this presentation is to prove that this rigidity result does not extend to higher dimensions and, more ... More
Improved Beckner-Sobolev inequalities on Kähler manifoldsMay 16 2019We prove new Beckner-Sobolev type inequalities on compact K\"{a}hler manifolds with positive Ricci curvature. As an application, we obtain a diameter upper bound that improves the Bonnet-Myers bound.
Filling metric spacesMay 16 2019We prove an inequality conjectured by Larry Guth that relates the $m$-dimensional Hausdorff content of a compact metric space with its $(m-1)$-dimensional Urysohn width. As a corollary, we obtain new systolic inequalities that both strengthen the classical ... More
On the extension of holomorphic sections from reduced unions of strata of divisorsMay 16 2019In this paper we study the problem of extension of holomorphic sections of line bundles/vector bundles from reduced unions of strata of divisors. An extension theorem of Ohsawa--Takegoshi type is proved. As consequences we deduce several qualitative results ... More
Isometric Immersions and the Waving of FlagsMay 15 2019In this article we propose a novel geometric model to study the motion of a physical flag. In our approach a flag is viewed as an isometric immersion from the square with values into $\mathbb R^3$ satisfying certain boundary conditions at the flag pole. ... More
The index of exceptional symmetric spacesMay 15 2019The index of a Riemannian symmetric space is the minimal codimension of a proper totally geodesic submanifold (Onishchik, 1980). There is a conjecture by the first two authors for how to calculate the index. In this paper we give an affirmative answer ... More
Higgs bundles and flat connections over compact Sasakian manifoldsMay 15 2019Given a compact K\"ahler manifold $X$, there is an equivalence of categories between the completely reducible flat vector bundles on $X$ and the polystable Higgs bundles $(E,\, \theta)$ on $X$ with $c_1(E)= 0= c_2(E)$ \cite{SimC}, \cite{Cor}, \cite{UY}, ... More
Conformal invariants from nodal sets II. Manifolds with boundaryMay 15 2019In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators on manifolds with boundary. We also consider applications to curvature prescription problems on manifolds with boundary. ... More
Notes on Projective, Contact, and Null CurvesMay 15 2019These are notes on some algebraic geometry of complex projective curves, together with an application to studying the contact curves in CP^3 and the null curves in the complex quadric Q^3 in CP^4, related by the well-known Klein correspondence. Most of ... More
Möbius invariant metrics on the space of knotsMay 15 2019We introduce a method to give M\"obius invariant weighted inner products on the tangent spaces of the space of non-circular knots by making use of M\"obius invariant energies of knots, by which we can obtain M\"obius invariant gradients of such energies. ... More
On O'hara knot energies I: Regularity for critical knotsMay 15 2019We develop a regularity theory for extremal knots of scale invariant knot energies defined by J. O'hara in 1991. This class contains as a special case the M\"obius energy. For the M\"obius energy, due to the celebrated work of Freedman, He, and Wang, ... More
Sign choices for orientifoldsMay 15 2019We analyse the problem of assigning sign choices to O-planes in orientifolds of type II string theory. We show that there exists a sequence of invariant $p$-gerbes with $p\geq-1$, which give rise to sign choices and are related by coboundary maps. We ... More
Geometry of universal embedding spaces for almost complex manifoldsMay 15 2019We study the geometry of universal embedding spaces for compact almost complex manifolds of a given dimension. These spaces are complex algebraic analogues of twistor spaces that were introduced by J-P. Demailly and H. Gaussier. Their original goal was ... More
Geometric Algorithm of Schrödinger Flow on a SphereMay 15 2019We construct the solution to the periodic Cauchy problem of the Schr\"odinger flow on the sphere. Such construction of solutions is formulated explicitly and therefore a geometric algorithm of solving this periodic Cauchy problem follows. Theoretical ... More
Mabuchi's soliton metric and relative D-stabilityMay 15 2019For Fano manifolds T. Mabuchi introduced a generalization of the K\"ahler-Einstein metric, which is characterized as the critical point of the Ricci-Calabi functional. We show that a Fano manifold admits Mabuchi's metric if and only if it is uniformly ... More
Einstein-like doubly warped product manifoldsMay 14 2019In this paper, it is proved that the factor manifolds $M_{i},i=1,2$ of a doubly warped product manifold $M=_{f_{2}}M_{1}\times _{f_{1}}M_{2}$ acquire the Einstein-like class type $\mathcal{A},$ $\mathcal{B}$ or $\mathcal{P}$ of $M$ by imposing a sufficient ... More
A note on time analyticity for ancient solutions of the heat equationMay 14 2019It is well known that generic solutions of the heat equation are not analytic in time in general. Here it is proven that ancient solutions with exponential growth are analytic in time in ${\M} \times (-\infty, 0]$. Here $\M=\R^n$ or is a manifold with ... More
Sliding Motions on SO(3), Sliding SubgroupsMay 14 2019We propose a sliding surface for systems on the Lie group $SO(3)\times \mathbb{R}^3$ . The sliding surface is shown to be a Lie subgroup. The reduced-order dynamics along the sliding subgroup have an almost globally asymptotically stable equilibrium. ... More
On the Morse Index of Branched Willmore Spheres in $3$-SpaceMay 14 2019We develop a general method to compute the Morse index of branched Willmore spheres and show that for immersions the Morse index is equal to a certain matrix whose dimension is equal to the number of end of the dual minimal surface. As a corollary, we ... More
Symplectic dominationMay 14 2019Let M be a compact oriented even-dimensional manifold. This note constructs a compact symplectic manifold S of the same dimension and a map f from S to M of strictly positive degree. The construction relies on two deep results: the first is a theorem ... More
1st eigenvalue pinching for convex hypersurfaces in a Riemannian manifoldMay 14 2019Let $M^n$ be a closed convex hypersurface lying in a convex ball $B(p,R)$ of the ambient $(n+1)$-manifold $N^{n+1}$. We prove that, by pinching Heintze-Reilly's inequality via sectional curvature upper bound of $B(p,R)$, 1st eigenvalue and mean curvature ... More
Contracting axially symmetric hypersurfaces by powers of the $σ_k$-curvatureMay 14 2019In this paper, we investigate the contracting curvature flow of closed, strictly convex axially symmetric hypersurfaces in $\mathbb{R}^{n+1}$ and $\mathbb{S}^{n+1}$ by $\sigma_k^\alpha$, where $\sigma_k$ is the $k$-th elementary symmetric function of ... More
Busemann functions on the Wasserstein spaceMay 14 2019We study rays and co-rays in the Wasserstein space $P_p(\mathcal{X})$ ($p > 1$) whose ambient space $\mathcal{X}$ is a complete, separable, non-compact, locally compact length space. We show that rays in the Wasserstein space can be represented as probability ... More
A fibration theorem for collapsing sequences of Alexandrov spacesMay 14 2019Let a sequence $M_j$ of Alexandrov spaces collapse to a space $X$ with only weak singularities. T. Yamaguchi constructed a map $f_j:M_j\to X$ for large $j$ called an almost Lipschitz submersion. We prove that if $M_j$ has a uniform positive lower bound ... More
Regular points of extremal subsets in Alexandrov spacesMay 14 2019We define regular points of an extremal subset in an Alexandrov space and study their basic properties. We show that a neighborhood of a regular point in an extremal subset is almost isometric to an open subset in the Euclidean space and that the set ... More
Sharp Poincaré inequality under Measure Contraction PropertyMay 14 2019We prove a sharp Poincar\'e inequality for subsets $\Omega$ of (essentially non-branching) metric measure spaces satisfying the Measure Contraction Property $\textrm{MCP}(K,N)$, whose diameter is bounded above by $D$. This is achieved by identifying the ... More
Uniformizing surfaces via discrete harmonic mapsMay 14 2019We show that for any closed surface of genus greater than one and for any finite weighted graph filling the surface, there exists a hyperbolic metric which realizes the least Dirichlet energy harmonic embedding of the graph among a fixed homotopy class ... More
A discrete approach to Wirtinger's inequalityMay 14 2019Considering Wirtinger's inequality for piece-wise equipartite functions we find a discrete version of this classical inequality. The main tool we use is the theorem of classification of isometries. Our approach provides a new elementary proof of Wirtinger's ... More
Homogeneous surfaces admitting invariant connectionsMay 14 2019We compute all the simply connected homogeneous and infinitesimally homogeneous surfaces admitting one or more invariant affine connections. We find exactly six non equivalent simply connected homogeneous surfaces admitting more than one invariant connections ... More
H-functional and Matsushima type decomposition theoremMay 14 2019The H-functional characterizes K\"ahler-Ricci solitons as its critical points, and also plays an important role of the existence problem for K\"ahler-Einstein metrics. In this paper we prove the Hessian formula for the H-functional at its critical points, ... More
H-functional and Matsushima type decomposition theoremMay 14 2019May 17 2019The H-functional characterizes K\"ahler-Ricci solitons as its critical points, and also plays an important role of the existence problem for K\"ahler-Einstein metrics. In this paper we prove the Hessian formula for the H-functional at its critical points, ... More
Desingularizing positive scalar curvature 4-manifoldsMay 13 2019We show that the bordism group of closed 3-manifolds with positive scalar curvature (psc) metrics is trivial by explicit methods. Our constructions are derived from scalar-flat K{\"a}hler ALE surfaces discovered by Lock-Viaclovsky. Next, we study psc ... More
Variational formulas for submanifolds of fixed degreeMay 13 2019We consider in this paper an area functional defined on submanifolds of fixed degree immersed into a graded manifold equipped with a Riemannian metric. Since the expression of this area depends on the degree, not all variations are admissible. It turns ... More
Transverse Kähler-Ricci flow and deformations of the metric on the Sasaki space $T^{1,1}$May 13 2019In this paper we investigate the possibility to obtain locally new Sasaki-Einstein metrics on the space $T^{1,1}$ considering a deformation of the standard metric tensor field. We show that from the geometric point of view this deformation leaves transverse ... More
The Lie group of vertical bisections of a regular Lie groupoidMay 13 2019In this note we construct an infinite-dimensional Lie group structure on the group of vertical bisections of a regular Lie groupoid. We then identify the Lie algebra of this group and discuss regularity properties (in the sense of Milnor) for these Lie ... More
On the Moduli Space of Null Curves in Klein's QuadricMay 13 2019We study the moduli space of null curves in Klein's quartic in the four-dimensional (complex) projective plane using methods developed by Robert Bryant. As a consequence, we show that minimal surfaces with $9$ embedded planar ends do not exist and formulate ... More
Positive curvature operator, projective manifold and rational connectednessMay 13 2019In his recent work \cite{Y1}, X. Yang proved a conjecture raised by Yau in 1982 (\cite{Yau82}), which states that any compact K\"{a}hler manifold with positive holomorphic sectional curvature must be projective. In this note, we prove that any compact ... More
A hyperbolic counterpart to Rokhlin's cobordism theoremMay 12 2019The purpose of the present note is to prove existence of super-exponentially many compact orientable hyperbolic arithmetic $n$-manifolds that are geometric boundaries of compact orientable hyperbolic $(n+1)$-manifolds, for each $2 \leq n \leq 8$, thereby ... More
A class of anisotropic expanding curvature flowsMay 12 2019We consider an expanding flow of smooth, closed, uniformly convex hypersurfaces in (n+1)-dimensional Euclidean space with speed fu^{alpha}{sigma}_k^{beta}, where u is the support function of the hypersurface, alpha, beta are two constants, and beta>0, ... More
An Anisotropic shrinking flow and L_p Minkowski problemMay 12 2019We consider a shrinking flow of smooth, closed, uniformly convex hypersurfaces in (n+1)-dimensional Euclidean space with speed fu^{alpha}{sigma}_n^{beta}, where u is the support function of the hypersurface, alpha, beta are two constants, and beta>0, ... More
Rectifying-type curves and rotation minimizing frame $R_{n}$May 11 2019In this paper, we have first given easily the characterization of special curves with the help of the Rotation minimizing frame (RMF). Also, rectifying-type curves are generalized n-dimensional space $R_{n}$.
On the Exponential Stability of Projected Primal-Dual Dynamics on a Riemannian ManifoldMay 11 2019Equivalence of convex optimization, saddle-point problems, and variational inequalities is a well-established concept. The variational inequality (VI) is a static problem which is studied under dynamical settings using a framework called the projected ... More
Systole on locally symmetric spacesMay 10 2019Here we survey on the growth of systoles of arithmetic locally symmetric spaces under the congruence covering and give simple proofs for the best possible constants of Gromov for several important classes of symmetric spaces.
Ricci-flat Kähler metrics on tangent bundles of rank-one symmetric spaces of compact typeMay 10 2019We give an explicit description of all complete $G$-invariant Ricci-flat K\"ahler metrics on the tangent bundle $T(G/K)\cong G^\bbC/K^\bbC$ of rank-one Riemannian symmetric spaces $G/K$ of compact type, in terms of associated vector-functions.
On the Index of Willmore spheresMay 10 2019We consider unbranched Willmore surfaces in the Euclidean space that arise as inverted complete minimal surfaces with embedded planar ends. Several statements are proven about upper and lower bounds on the Morse Index - the number of linearly independent ... More
On the Index of Willmore spheresMay 10 2019May 22 2019We consider unbranched Willmore surfaces in the Euclidean space that arise as inverted complete minimal surfaces with embedded planar ends. Several statements are proven about upper and lower bounds on the Morse Index - the number of linearly independent ... More
Non-symmetric Riemannian gravity and Sasaki-Einstein 5-manifoldsMay 10 2019We show that a connection with skew-symmetric torsion satisfying the Einstein metricity condition exists on an almost contact metric manifold exactly when it is D-homothetic to a cosymplectic manifold. In dimension five, we get that the existence of a ... More
Filtered instanton Floer homology and the homology cobordism groupMay 10 2019For any $s \in \mathbb{R}_{\leq 0} \cup \{-\infty\}$ and oriented homology $3$-sphere $Y$ , we introduce a homology cobordism invariant $r_s(Y )$ whose value is in $ \mathbb{R}_{>0} \cup \{\infty \}$. The values $\{r_s (Y )\}$ are contained in the critical ... More
Real Kähler Submanifolds in Codimension $6$May 09 2019May 14 2019We show that a real K\"ahler submanifold in codimension $6$ is essentially a holomorphic submanifold of another real K\"ahler submanifold in lower codimension if the second fundamental form is not sufficiently degenerated. We also give a shorter proof ... More
The Mean Curvature of First-Order Submanifolds in Geometries with TorsionMay 09 2019We derive formulas for the mean curvature of special Lagrangian 3-folds, associative 3-folds, and coassociative 4-folds in the general case where the ambient space has intrinsic torsion. Consequently, we are able to characterize those SU(3)-structures ... More
Isotropic quasi-Einstein manifoldsMay 09 2019We investigate the local structure of four-dimensional Lorentzian quasi-Einstein manifolds under conditions on the Weyl tensor. We show that if the Weyl tensor is harmonic and the potential function preserves this harmonicity then, in the isotropic case, ... More
Lagrangian fibrations by Prym varietiesMay 08 2019We survey Lagrangian fibrations of holomorphic symplectic varieties, both compact and non-compact, whose fibres are Jacobians and Prym varieties.
A Henstock-Kurzweil type integral on 1 dimensional integral currentsMay 08 2019We define a non-absolutely convergent integration on integral currents of dimension 1 in Euclidean space. This integral is closely related to the Henstock-Kurzweil and Pfeffer Integrals. Using it, we prove a generalized Fundamental Theorem of Calculus ... More
Fundamental theorem of spacelike curves in Lorentz-Minkowski spaceMay 08 2019In Lorentz-Minkowski 3-space, the fundamental theorem of spacelike curves is known, if they have spacelike, timelike or lightlike curvature vector fields. However, such a theory cannot be applied to spacelike curves with type-changing curvature vector ... More
Upper bounds on Renormalized Volume for Schottky groupsMay 08 2019In this article we show that for any given Riemann surface $\Sigma$ of genus $g$, we can bound (from above) the renormalized volume of a (hyperbolic) Schottky group with boundary at infinity conformal to $\Sigma$ in terms of the genus and the combined ... More
The Fourier transform on harmonic manifolds of purely exponential volume growthMay 08 2019Let $X$ be a complete, simply connected harmonic manifold of purely exponential volume growth. This class contains all non-flat harmonic manifolds of non-positive curvature and, in particular all known examples of harmonic manifolds except for the flat ... More
On the asymptotic Plateau problem for area minimizing surfaces in $\mathbb{E}(-1,τ)$May 08 2019We prove some existence and non-existence results for complete area minimizing surfaces in the homogeneous space $\mathbb{E}(-1,\tau)$. As one of our main results, we present sufficient conditions for a curve $\Gamma$ in $\partial_{\infty} \mathbb{E}(-1,\tau)$ ... More
Index of minimal spheres and isoperimetric eigenvalue inequalitiesMay 08 2019In the present paper we use twistor theory in order to solve two problems related to harmonic maps from surfaces to Euclidean spheres $\mathbb{S}^n$. First, we propose a new approach to isoperimetric inequalities based on energy index. Using this approach ... More
The contact structure induced by a line fibration of R^3 is standardMay 08 2019Building on the work of and answering a question by Michael Harrison, we show that any contact structure on Euclidean 3-space induced by a line fibration is diffeomorphic to the standard contact structure.
BigerbesMay 08 2019Bigerbes give a refinement of the notion of 2-gerbes, representing degree four integral cohomology classes of a space. Defined in terms of bisimplicial line bundles, bigerbes have a symmetry with respect to which they form 'bundle 2-gerbes' in two ways; ... More
Nearly parallel $G_2$-structures with large symmetry groupMay 08 2019We prove the existence of a one-parameter family of nearly parallel $G_2$-structures on the manifold $S^3\times \mathbb R^4$, which are mutually non isomorphic and invariant under the cohomogeneity one action of the group $SU(2)^3$. This family connects ... More
Smooth classifying spaces for differential $K$-theoryMay 08 2019We construct a version of differential $K$-theory based on smooth Banach manifold models for the homotopy types $B \mathrm U\times Z$ and $\mathrm U$ that appear in the topological $K$-theory spectrum. These manifolds carry natural differential forms ... More
Geometric quantization of Hamiltonian flows and the Gutzwiller trace formulaMay 08 2019We use the theory of Berezin-Toeplitz operators of Ma and Marinescu to study the quantum Hamiltonian dynamics associated with classical Hamiltonian flows over closed prequantized symplectic manifolds in the context of geometric quantization of Kostant ... More
Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metricsMay 08 2019We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics. We prove that a compact locally conformal K\"{a}hler manifold with constant nonpositive holomorphic sectional curvature is K\"{a}hler. We ... More
Time-dependent scattering theory on manifoldsMay 08 2019Based on our previous study [IS3] on the stationary scattering theory for the Schrodinger operator on a manifold possessing an escape function we complete our investigation by doing the time-dependent counterpart. A particular class of examples are manifolds ... More
On A Fully Nonlinear Equation in Relativistic Teichmüller TheoryMay 08 2019We obtain basic estimates for a Monge-Amp\`{e}re equation introduced by Moncrief in the study of the Relativistic Teichm\"{u}ller Theory. We then give another proof of the parametrization of the Teichm\"uller space obtained by Moncrief. Our approach provides ... More
Geodesic mappings and concircular vector fieldsMay 07 2019In the present paper we study geodesic mappings of special pseudo-Riemannian manifolds called $V_n(K)$-spaces. We prove that the set of solutions of the system of equations of geodesic mappings on $V_n(K)$-spaces $(K\neq0)$ forms a special Jordan algebra ... More
Twisted Dolbeault cohomology of nilpotent Lie algebrasMay 07 2019It is well known that cohomology of any non-trivial 1-dimensional local system on a nilmanifold vanishes (this result is due to L. Alaniya). A complex nilmanifold is a quotient of a nilpotent Lie group equipped with a left-invariant complex structure ... More
Locally conformally symplectic reduction of the cotangent bundleMay 07 2019In a previous article, we introduced a reduction procedure for locally conformally symplectic manifolds at any regular value of the momentum mapping. We use this construction to prove an analogue of a well-known theorem in the symplectic setting about ... More
Gradient estimate for harmonic functions on Kähler manifoldsMay 07 2019We prove a sharp integral gradient estimate for harmonic functions on noncompact K\"ahler manifolds. As application, we obtain a sharp estimate for the bottom of spectrum of the p-Laplacian and prove a splitting theorem for manifolds achieving this estimate. ... More
Entropies for negatively curved manifoldsMay 07 2019We survey several notions of entropy related to a compact manifold of negative curvature, some relations between them, and the rigidity problems.
Equivariant holonomy of U(1)-bundlesMay 07 2019We define the equivariant holonomy of an invariant connection on a principal U(1)-bundle. The properties of the ordinary holonomy are generalized to the equivariant setting. In particular, equivariant U(1)-bundles with connection are shown to be classified ... More
Weak Continuity of the Cartan Structural System on Semi-Riemannian Manifolds with Lower RegularityMay 07 2019We are concerned with the global weak continuity of the Cartan structural system - or equivalently, the Gauss-Codazzi-Ricci system - on semi-Riemannian manifolds. We prove the $W^{2,p}$ weak continuity of the Cartan structural system for $p>2$: For a ... More
Determining the geometry of noncircular gears for given transmission functionMay 07 2019A pair of noncircular gears can be used to generate a strictly increasing continuous function $\psi(\varphi)$ whose derivative $\psi'(\varphi) = \mathrm{d}\psi(\varphi)/\mathrm{d}\varphi > 0$ is $2\pi/n$-periodic, where $\varphi$ and $\gamma = \psi(\varphi)$ ... More
On metrics of constant positive curvature with four conic singularities on the sphereMay 07 2019We show that for given four points on the sphere and prescribed angles at these points, which are not multiples of $2\pi$, the number of metrics of curvature 1 having conic singularities with these angles at these points is finite.
Global controllability tests for geometric hybrid control systemsMay 07 2019Hybrid systems are characterized by having an interaction between continuous dynamics and discrete events. The contribution of this paper is to provide hybrid systems with a novel geometric formulation so that controls can be added. Using this framework ... More
Momentum sections in Hamiltonian mechanics and sigma modelsMay 07 2019We show a constrained Hamiltonian system and a gauged sigma model have a structure of a momentum section and a Hamiltonian Lie algebroid theory recently introduced by Blohmann and Weinstein. We propose a generalization of a momentum section on a pre-multisymplectic ... More