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Integration by parts formula for non-pluripolar productJul 15 2019In this paper, we prove the integration by parts formula for the non-pluripolar product on a compact K\"ahler manifold. Our result generalizes the special case of potentials with small unbounded loci proved in [BEGZ10]. Weyl symbols and boundedness of Toeplitz operatorsJul 13 2019We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding Weyl symbols. Further remarks on rigidity of Hénon mapsJul 11 2019For a H\'{e}non map $H$ in $\mathbb{C}^2$, we characterize the polynomial automorphisms of $\mathbb{C}^2$ which keep any fixed level set of the Green function of $H$ completely invariant. The interior of any non-zero sublevel set of the Green function ... More An equilibrium problem on the sphere with two equal chargesJul 10 2019We study the equilibrium measure on the two dimensional sphere in the presence of an external field generated by two equal point charges. The support of the equilibrium measure is known as the droplet. Brauchart et al. showed that the complement of the ... More A Projectional Ansatz to ReconstructionJul 10 2019Recently the field of inverse problems has seen a growing usage of mathematically only partially understood learned and non-learned priors. Based on first principles we develop a projectional approach to inverse problems which addresses the incorporation ... More Noncommutative Schur-type products and their Schoenberg theoremJul 10 2019Schoenberg showed that a function $f:(-1,1)\rightarrow \mathbb{R}$ such that $C=[c_{ij}]_{i,j}$ positive semi-definite implies that $f(C)=[f(c_{ij})]_{i,j}$ is also positive semi-definite must be analytic and have Taylor series coefficients nonnegative ... More Wandering domains arising from Lavaurs maps with Siegel disksJul 09 2019The classification of Fatou components for rational functions was concluded with Sullivan's proof of the No Wandering Domains Theorem in 1985. In 2016 it was shown, in joint work of the first and last author with Buff, Dujardin and Raissy, that wandering ... More On Competing Definitions for the Diederich-Fornæss IndexJul 08 2019Let $\Omega\subset\mathbb{C}^n$ be a bounded pseudoconvex domain. We define the Diederich-Forn{\ae}ss index with respect to a family of functions to be the supremum over the set of all exponents $0<\eta<1$ such that there exists a function $\rho_\eta$ ... More Gluing Theorems for Subharmonic FunctionsJul 07 2019Jul 12 2019In our articles of recent years, the technique of gluing two subharmonic functions turned out to be very useful in studying the distribution of the roots or masses of holomorphic or subharmonic functions, respectively. Here we develop and improve this ... More Gluing Theorems for Subharmonic FunctionsJul 07 2019In our articles of recent years, the technique of gluing two subharmonic functions turned out to be very useful in studying the distribution of the roots or masses of holomorphic or subharmonic functions, respectively. Here we develop and improve this ... More Bilevel Integrative Optimization for Ill-posed Inverse ProblemsJul 06 2019Classical optimization techniques often formulate the feasibility of the problems as set, equality or inequality constraints. However, explicitly designing these constraints is indeed challenging for complex real-world applications and too strict constraints ... More Construction of labyrinths in pseudoconvex domainsJul 05 2019We build in a given pseudoconvex (Runge) domain $D$ of $\mathbb{C}^N$ a $\mathcal O(D)$ convex set $\Gamma$, every connected component of which is a holomorphically contractible (convex) compact set, enjoying the property that any continuous path $\gamma:[0,1)\rightarrow ... More On the continuous extension of Kobayashi isometriesJul 04 2019We provide a sufficient condition for the continuous extension of isometries for the Kobayashi distance between bounded convex domains in complex Euclidean spaces having boundaries that are only slightly more regular than $\mathcal{C}^1$. This is a generalization ... More Quaternionic Analysis, Representation Theory and Physics IIJul 02 2019We develop further quaternionic analysis introducing left and right doubly regular functions. We derive Cauchy-Fueter type formulas for these doubly regular functions that can be regarded as another counterpart of Cauchy's integral formula for the second ... More Entire functions polynomially bounded in several variablesJul 01 2019In this paper we show that if an entire function $f(z_1,z_2)$ of two (or more) complex variables verifies $\norm{f(z_1,z_2)}\leq K(\norm{P(z_1,z_2)})$, where $P(z_1,z_2)$ is a polynomial that is not a power in $\CC[[z_1,z_2]]$, and $K$ is any positive-valued ... More Polynomial approximation avoiding values in countable setsJun 29 2019We generalize a version of Lavrent\'ev's theorem which says that a function that is continuous on a compact set K with connected complement and without interior points can be uniformly approximated as closely as desired by a polynomial without zeros on ... More Some properties of $h$-extendible domains in $\mathbb C^{n+1}$Jun 29 2019Jul 06 2019The purpose of this article is twofold. The first aim is to characterize $h$-extendibility of smoothly bounded pseudoconvex domains in $\mathbb C^{n+1}$ by their noncompact automorphism groups. Our second goal is to show that if the squeezing function ... More Some properties of $H$-extendible domains in $\mathbb C^{n+1}$Jun 29 2019The purpose of this article is twofold. The first aim is to characterize $h$-extendibility of smoothly bounded pseudoconvex domains in $\mathbb C^{n+1}$ by their noncompact automorphism groups. Our second goal is to show that if the squeezing function ... More Subharmonicity of direct images and applicationsJun 26 2019In this article we establish new positivity properties for direct images of twisted pluricanonical bundle of an algebraic fiber space. As a corollary we obtain an algebraicity criteria for holomorphic foliations which partly confirms a conjecture of Pereira-Touzet. ... More Singularities of rational inner functions in higher dimensionsJun 26 2019We study the boundary behavior of rational inner functions (RIFs) in dimensions three and higher from both analytic and geometric viewpoints. On the analytic side, we use the critical integrability of the derivative of a rational inner function of several ... More Improved Hölder regularity for strongly elliptic PDEsJun 26 2019We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new relations between ... More Kähler-Einstein metrics on symmetric general arrangement varietiesJun 24 2019Jul 03 2019We calculate Chow quotients of some families of symmetric \(T\)-varieties. In complexity two we obtain new examples of K\"ahler-Einstein metrics by bounding the symmetric alpha invariant of their orbifold quotients. As an additional application we determine ... More Kähler-Einstein metrics on symmetric general arrangement varietiesJun 24 2019Jun 29 2019We calculate Chow quotients of some families of symmetric \(T\)-varieties. In complexity two we obtain new examples of K\"ahler-Einstein metrics by bounding the symmetric alpha invariant of their orbifold quotients. As an additional application we determine ... More The complex Monge-Ampère equation with a gradient termJun 24 2019We consider the complex Monge-Amp\`ere equation with an additional linear gradient term inside the determinant. We prove existence and uniqueness of solutions to this equation on compact Hermitian manifolds. On Lisbon integralsJun 24 2019We introduce a family of integral transforms, the Lisbon Integrals, which naturally arise in the study of the affine space of unitary polynomials P s (z) where s $\in$ C k and z $\in$ C, s i identified to the i-th symmetric function of the roots of P ... More On Lisbon integralsJun 24 2019Jun 26 2019We introduce a family of integral transforms, the Lisbon Integrals, which naturally arise in the study of the affine space of unitary polynomials P s (z) where s $\in$ C k and z $\in$ C, s i identified to the i-th symmetric function of the roots of P ... More Relative regular Riemann-Hilbert correspondenceJun 24 2019In previous works by the last named authors, the notion of regularity for a relative holonomic $\mathcal D$-module has been introduced, as well as that of relative constructible complex, and it has been proved that, if the parameter space has dimension ... More On the genesis of BBP formulasJun 23 2019We present a general procedure to generate infinitely many BBP and BBP-like formulas for the simplest transcendental numbers. This provides some insight and a better understanding into their nature. In particular, we can derive the main known BBP formulas ... More Morse-type integrals on non-Kähler manifoldsJun 23 2019We pose a conjecture about Morse-type integrals in nef (1,1) classes on compact Hermitian manifolds, and we show that it holds for semipositive classes, or when the manifold admits certain special Hermitian metrics. The solution of the Brannan conjectureJun 22 2019We make the final step to give a proof for the Brannan's conjecture. The basic tool of the study is a Mac-Laurin development and an adequately estimation of an integral. Learning the Sampling Pattern for MRIJun 20 2019The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long acquisition times ... More Transcendental versions in C n of the Nagata conjectureJun 20 2019The Nagata Conjecture is one of the most intriguing open problems in the area of curves in the plane. It is easily stated. Namely, it predicts that the smallest degree d of a plane curve passing through r $\ge$ 10 general points in the projective plane ... More XNAS: Neural Architecture Search with Expert AdviceJun 19 2019This paper introduces a novel optimization method for differential neural architecture search, based on the theory of prediction with expert advice. Its optimization criterion is well fitted for an architecture-selection, i.e., it minimizes the regret ... More Holomorphic one-forms without zeros on threefoldsJun 18 2019We show that a smooth complex projective threefold admits a holomorphic one-form without zeros if and only if the underlying real 6-manifold fibres smoothly over the circle, and we give a complete classification of all threefolds with that property. Our ... More Zeros of holomorphic one-forms and topology of Kähler manifoldsJun 18 2019A conjecture of Kotschick predicts that a compact K\"ahler manifold $X$ fibres smoothly over the circle if and only if it admits a holomorphic one-form without zeros. In this paper we develop an approach to this conjecture and verify it in dimension two. ... More A Kollár-type vanishing theoremJun 18 2019Jun 19 2019Let $f:X\rightarrow Y$ be a smooth fibration between two complex manifolds $X$ and $Y$, and let $L$ be a pseudo-effective line bundle on $X$. We obtain a sufficient condition for $R^{q}f_{\ast}(K_{X/Y}\otimes L)$ to be reflexive and hence derive a Koll\'{a}r-type ... More Siegel disks of the tangent familyJun 17 2019We study Siegel disks in the dynamics of functions from the tangent family. In particular, we prove that a forward invariant Siegel disk is unbounded if and only if it contains at least one asymptotic value on the boundary. Our argument is elementary ... More Computing Theta Functions with JuliaJun 15 2019We present a new package Theta.jl for computing with the Riemann theta function. It is implemented in Julia and offers accurate numerical evaluation of theta functions with characteristics and their derivatives of arbitrary order. Our package is optimized ... More Bounded sets of sheaves on Kähler manifolds, IIJun 13 2019We extend previous results on boundedness of sets of coherent sheaves on a compact K\"ahler manifold to the relative and not necessarily smooth case. This enlarged context allows us to prove properness properties of the relative Douady space as well as ... More Time warping invariants of multidimensional time seriesJun 13 2019In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, in a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe ... More Geometric quantization on CR manifoldsJun 13 2019Let $X$ be a compact connected orientable CR manifold of dimension greater than five with the action of a connected compact Lie group $G$. Assuming that the Levi form of $X$ is positive definite near the inverse image $Y$ of $0$ by the momentum map and ... More Geometric quantization on CR manifoldsJun 13 2019Jun 17 2019Let $X$ be a compact connected orientable CR manifold of dimension greater than five with the action of a connected compact Lie group $G$. Assuming that the Levi form of $X$ is positive definite near the inverse image $Y$ of $0$ by the momentum map and ... More