Related papers: Biholomorphic mapping on the boundary I
In this article, we study holomorphic isometric embeddings between bounded symmetric domains. In particular, we show the total geodesy of any holomorphic isometric embedding between reducible bounded symmetric domains with the same rank.
We characterize pairs of bounded Reinhardt domains in $\CC^2$ between which there exists a proper holomorphic map and find all proper maps that are not elementary algebraic.
We consider proper holomorphic maps of ball complements and differences in complex euclidean spaces of dimension at least two. Such maps are always rational, which naturally leads to a related problem of classifying rational maps taking…
We prove that given a family of strictly pseudoconvex domains varying in C2 topology on domains, there exists a continuously varying family of exposing maps for all boundary points of all domains.
It is studied the Classification Problem for Formal (Holomorphic) Embeddings between (open pieces of) Shilov Boundaries of Bounded Symmetric Domains of First Type.
We study inequalities between the hyperbolic metric and intrinsic metrics in convex polygonal domains in the complex plane. Special attention is paid to the triangular ratio metric in rectangles. A local study leads to an investigation of…
We study the boundary behaviour of a variant of the Fridman's invariant function (defined in terms of the Bergman metric) on Levi corank one domains, strongly pseudoconvex domains, smoothly bounded convex domains in $ \mathbb{C}^n $ and…
More precise estimates for the Bergman metric on strongly pseudoconvex domains are given, based on the use of the squeezing function.
We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…
We show that for any bounded domain $\Omega\subset\Cp ^n$ of 1-type $2k $ which is locally convexifiable at $p\in b\Omega$, having a Stein neighborhood basis, there is a biholomorphic map $f:\bar{\Omega}\rightarrow \Cp ^n $ such that $f(p)$…
We prove optimal estimates of the Bergman and Szeg\H{o} kernels on the diagonal, and the Bergman metric near the boundary of bounded smooth generalized decoupled pseudoconvex domains in $\mathbb{C}^n$. The generalized decoupled domains we…
The purpose of this article is to consider two themes both of which emanate from and involve the Kobayashi and the Carath\'eodory metric. First we study the biholomorphic invariant introduced by B. Fridman on strongly pseudoconvex domains,…
Let $\Omega$ be a proper open cone in a real Banach space $V$. We show that the tube domain $V \oplus i\Omega$ over $\Omega$ is biholomorphic to a bounded symmetric domain if and only if $\Omega$ is a normal linearly homogeneous Finsler…
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.
We show that there are many sets in the boundary of a bounded symmetric domain that determine the values and norm of holomorphic functions on the domain having continuous extensions to the boundary. We provide an analogue of the…
We review recent progress on two closely related sets of questions concerning convex co-compact hyperbolic manifolds, or convex domains in those manifolds, such as their convex core. The first set of questions is to what extent the…
In this paper we construct a properly embedded holomorphic disc in the unit ball $\mathbb{B}^2$ of $\mathbb{C}^2$ having a surprising combination of properties: on the one hand, it has finite area and hence is the zero set of a bounded…
In a previous work on the large $|k|$ behavior of complex geometric optics solutions to a system of d-bar equations, we treated in detail the situation when a certain potential is the characteristic function of a strictly convex set with…
We study the image and the singularity subset of a general pseudoholomorphic map. We show that the image of a proper pseudoholomorphic map is a pseudoholomorphic subvariety when the dimension of either the domain or target is four. We also…
An example is given of a hyperconvex manifold without non-constant bounded holomorphic functions, which is realized as a domain with real-analytic Levi-flat boundary in a projective surface.