Related papers: On the squeezing function and Fridman invariants
A quantitative version of strong localization of the Kobayashi, Azukawa and Sibony metrics, as well as of the squeezing function, near a plurisubharmonic peak boundary point of a domain in $\Bbb C^n$ is given. As an application, the…
It is shown that if the squeezing function tends to one at an h-extendible boundary point of a $\mathcal C^\infty$-smooth, bounded pseudoconvex domain, then the point is strictly pseudoconvex.
The main purpose of the present paper is to introduce the notion of squeezing functions of bounded domains and study some properties of them. The relation to geometric and analytic structures of bounded domains will be investigated.…
We prove two separate lower bounds -- one for nondegenerate convex domains and the other for nondegenerate $\mathbb{C}$-convex (but not necessarily convex) domains -- for the squeezing function that hold true for all domains in…
We give estimates for the squeezing function on strictly pseudoconvex domains, and derive some sharp estimates for the Caratheodory, Sibony and Azukawa metric near their boundaries.
We study a variant of the Alt, Caffarelli, and Friedman free boundary problem with many phases and a slightly different volume term, which we originally designed to guess the localization of eigenfunctions of a Schr\"odinger operator in a…
Let $D$ be a bounded domain in $\mathbb C^n$. We study approximation of (not necessarily bounded from above) $m-$subharmonic function $D$ by continuous $m-$subharmonic ones defined on neighborhoods of $\overline{D}$. We also consider the…
We pose some open problems related to boundedness of real-valued functions on balleans and coarse spaces. Also we prove that the Bergman property of groups is a coarse invariant. A special attention is payed to balleans on groups.
The 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…
This note investigates the relation between squeezing function and its generalizations. Using the relation obtained, we present an alternate method to find expression of generalized squeezing function of unit ball corresponding to 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…
Very recently, the Fridman function of a complex manifold $X$ has been identified as a dual of the squeezing function of $X$. In this paper, we prove that the Fridman function for certain hyperbolic complex manifold $X$ is bounded above by…
We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…
We study bounded domains with certain smoothness conditions and the properties of their squeezing functions in order to prove that the domains are biholomorphic to the ball.
Comparison and localization results for the Lempert function, the Carath\'eodory distance and their infinitesimal forms on strongly pseudoconvex domains are obtained. Related results for visible and strongly complete domains are proved.
Invariant functions and metrics are studied on various classes of domains in $\Bbb C^n.$
Two-sided bounds for the efficiency of the torsion function are obtained in terms of the square of the distance to the boundary function under the hypothesis that the Dirichlet Laplacian satisfies a strong Hardy inequality. Localisation…
Precise behavior of the Caratheodory, Kobayashi and Bergman metrics and distances near smooth boundary points of domains in C is found under different assumptions of regularity.
Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…