Related papers: Proper holomorphic mappings vs. peak points and Si…

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…

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.

In this article we consider area preserving diffeomorphisms of planar domains, and we are interested in their conformal points, i.e., points at which the derivative is a similarity. We present some conditions that guarantee existence of…

In this paper, we investigate the characterization of balanced bounded convex domains in $\mathbb{C}^n$ in terms of the squeezing function. As an application, we provide a characterization of the polydisc in $\mathbb{C}^n$.

In this paper, we prove necessary and sufficient conditions for a sense-preserving harmonic function to be absolutely convex in the open unit disk. We also estimate the coefficient bound and obtain growth, covering and area theorems for…

For a smoothly bounded pseudoconvex domain $D\subset{\Bbb C}^n$ of finite type with non-compact holomorphic automorphism group $\text{Aut}(D)$, we show that the set $S(D)$ of all boundary accumulation points for $\text{Aut}(D)$ is a compact…

Let D be a bounded strongly pseudoconvex domain in a Stein manifold S and let Y be a complex manifold. We prove that the graph of any continuous map from the closure of D to Y which is holomorphic in D admits a basis of open Stein…

We show that the $\bar{\partial}$-problem is globally regular on a domain in $\mathbb{C}^n$, which is the $n$-fold symmetric product of a smoothly bounded planar domain. Remmert-Stein type theorems are proved for proper holomorphic maps…

For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…

In this article, we introduce a new family of sense preserving harmonic mappings f in the open unit disk and prove that functions in this family are close-to-convex. We give some basic properties such as coefficient bounds, growth…

Given a fixed-point free compact holomorphic self-map $f$ on a bounded symmetric domain $D$, which may be infinite dimensional, we establish the existence of a family $\{H(\xi, \lambda)\}_{\lambda >0}$ of convex $f$-invariant domains at a…

We establish some estimates of the the angular derivatives from below for holomorphic self-maps of the unit disk at one and two fixed points of the unit circle provided there is no fixed point inside the unit disk. The results complement…

Given a bounded symmetric domain $D$, we study (positive) pluriharmonic functions on $D$ and investigate a possible analogue of the family of Clark measures associated with a holomorphic function from $D$ into the unit disc in $\mathbb C$.

We show that the first order Sobolev spaces on cuspidal symmetric domains can be characterized via pointwise inequalities. In particular, they coincide with the Hajlasz-Sobolev spaces.

We show that every bounded domain $D$ in $\mathbb R^n$ with smooth $p$-convex boundary for $2\le p < n$ admits a smooth defining function $\rho$ which is $p$-plurisubharmonic on $\overline D$; if in addition $bD$ has no $p$-flat points then…

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…

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…

Let $X, Y$ be smooth algebraic varieties of the same dimension. Let $f, g : X \to Y$ be finite polynomial mappings. We say that $f, g$ are equivalent if there exists a regular automorphism $\Phi \in Aut(X)$ such that $f = g\circ \Phi$. Of…

We introduce the notion of extremal basis of tangent vector fields at a boundary point of finite type of a pseudo-convex domain in $\mathbb{C}^n$. Then we define the class of geometrically separated domains at a boundary point, and give a…

Teichm\"uller's classical mapping problem for plane domains concerns finding a lower bound for the maximal dilatation of a quasiconformal homeomorphism which holds the boundary pointwise fixed, maps the domain onto itself, and maps a given…