Related papers: Explicit universal bounds for squeezing functions …

We consider the class of smooth convex functions defined over an open convex set. We show that this class is essentially different than the class of smooth convex functions defined over the entire linear space by exhibiting a function that…

In this article we prove the subrank of a generic tensor in $\mathbb{C}^{n,n,n}$ to be $Q(n) = \lfloor\sqrt{3n - 2}\rfloor$ by providing a lower bound to the known upper bound. More generally, we find the generic subrank of tensors of all…

Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…

Assume that $D\subset \R^2$ is a strictly convex domain with $C^2-$smooth boundary. {\bf Theorem.} {\em If $\int_De^{ix}y^ndxdy=0$ for all sufficiently large $n$, then $D$ is a disc.}

In this paper, we study constraint qualifications for the nonconvex inequality defined by a proper lower semicontinuous function. These constraint qualifications involve the generalized construction of normal cones and subdifferentials.…

We give a short proof of Wolff-Denjoy theorem for (not necessarily smooth) strictly convex domains. With similar techniques we are also able to prove a Wolff-Denjoy theorem for weakly convex domains, again without any smoothness assumption…

We derive optimal estimates for the Bergman kernel and the Bergman metric for certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. Being unbounded models, these domains obey certain geometric constraints…

The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the…

Let $D$ be a domain in a finite-dimensional Euclidean space, and $H$ be a convex subcone in the convex cone of all subharmonic functions on $D$. We obtain a criterion for the existence of a lower envelope from $H$ for an arbitrary function…

In this work we address the question of the existence of nonradial domains inside a nonconvex cone for which a mixed boundary overdetermined problem admits a solution. Our approach is variational, and consists in proving the existence of…

Given a subset $S=\{s_0, s_1\}$ of the complex plane with two points and an infinite subset ${\mathscr S}$ of $S\times {\mathbb N}$, where ${\mathbb N}=\{0,1,2,\dots\}$ is the set of nonnegative integers, we ask for a lower bound for the…

The Levi geometry at weakly pseudoconvex boundary points of domains in C^n, n \geq 3, is sufficiently complicated that there are no universal model domains with which to compare a general domain. Good models may be constructed by bumping…

In this article we continue the research, carried out in \cite{zajac}, on computing the $*$-product of domains in $\CC^N$. Assuming that $0\in G\subset\CC^N$ is an arbitrary Runge domain and $0\in D\subset\CC^N$ is a bounded, smooth and…

The softmax function is a ubiquitous component at the output of neural networks and increasingly in intermediate layers as well. This paper provides convex lower bounds and concave upper bounds on the softmax function, which are compatible…

We prove a generalization of the second variation formula of the Robin function associated to a smooth variation of domains in C^N to the case of the c-Robin function associated to a smooth variation of domains in a complex manifold M…

It is proved for a strongly pseudoconvex domain $D$ in $\Bbb C^d$ with $\mathcal C^{2,\alpha}$-smooth boundary that any complex geodesic through every two close points of $D$ sufficiently close to $\partial D$ and whose difference is…

We investigate the convexity up to symplectomorphism (called symplectic convexity) of star-shaped toric domains in $\mathbb R^4$. In particular, based on the criterion from Chaidez-Edtmair via Ruelle invariant and systolic ratio of the…

We show that if a bounded domain $\Omega$ is exhausted by a bounded strictly pseudoconvex domain $D$ with $C^2$ boundary, then $\Omega$ is holomorphically equivalent to $D$ or the unit ball, and show that a bounded domain has to be…

We prove conditions for the existence of a continuous linear right inverse for a surjective convolution operator in spaces of germs of analytic functions on convex subsets of the complex plane. Considered convex sets have a countable…

We prove regularity of solutions of the $\bar\partial$-problem in the H\"older-Zygmund spaces of bounded, strongly $\mathbf C$-linearly convex domains of class $C^{1,1}$. The proofs rely on a new, analytic characterization of said domains…