Related papers: Holomorphic Extendibility and Mapping Degree

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 establish rigidity results for holomorphic mappings and plurisubharmonic functions in complex geometry. First, under mild conditions, we show that the gradient of a $\operatorname{U}(1)$-invariant strictly plurisubharmonic function in…

We begin this note with a von Neumann algebraic version of the elementary but extremely useful fact about being able to extend inner-product preserving maps from a total set of the domain Hilbert space to an isometry defined on the entire…

We present new completeness conditions for exponential systems on the complex plane in Banach algebras of continuous functions on a compact with a connected complement that are simultaneously holomorphic in the interior of this compact if…

We study the regularity results of holomorphic correspondences. As an application, we combine it with certain recently developed methods to obtain the extension theorem for proper holomorphic mappings between domains with real analytic…

If $V$ is an analytic set in a pseudoconvex domain $\Omega$, we show there is always a pseudoconvex domain $G \subseteq \Omega$ that contains $V$ and has the property that every bounded holomorphic function on $V$ extends to a bounded…

This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques…

Consider the self-map F of the space of real-valued test functions on the line which takes a test function f to the test function sending a real number x to f(f(x))-f(0). We show that F is discontinuous, although its restriction to the…

We consider the problem of constructing a weakly-continuous mapping extending continuous mapping defined on a dense set of a topological space to the entire space. Theorem on necessary and sufficient conditions for the existence of such an…

Let $\alpha$ \in (0; 1). We show that any $\alpha$-H\"older homeomorphism from the unit circle in the plane to the plane can be extended to an $\alpha$-H\"{o}lder homeomorphism from the whole unit disc.

In this paper, we study the representation of orthogonally additive mappings acting on Hilbert $C^*$-modules and Hilbert $H^*$-modules. One of our main results shows that every continuous orthogonally additive mapping $f$ from a Hilbert…

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…

Let $D, G\subset{\Bbb C}$ be domains, let $A\subset D$, $B\subset G$ be locally regular sets, and let $X:=(D\times B)\cup(A\times G)$. Assume that $A$ is a Borel set. Let $M$ be a proper analytic subset of an open neighborhood of $X$. Then…

A graph admitting a perfect matching has the Perfect-Matching-Hamiltonian property (for short the PMH-property) if each of its perfect matchings can be extended to a Hamiltonian cycle. In this paper we establish some sufficient conditions…

Let $M$ be a closed surface and $f$ a diffeomorphism of $M$. A diffeomorphism is said to permute a dense collection of domains, if the union of the domains are dense and the iterates of any one domain are mutually disjoint. In this note, we…

The holomorphic endomorphism f of projective space is called post-critically finite (PCF) if the forward image of the critical locus, under iteration of f, has algebraic support (i.e., is a finite union of hypersurfaces). In the case of…

Let $M, M'$ be smooth, real analytic hypersurfaces of finite type in ${\mbf C^n}$ and $\h f$ a holomorphic correspondence (not necessarily proper) that is defined on one side of $M$, extends continuously up to $M$ and maps $M$ to $M'$. It…

Let f be a nonconstant meromorphic function in the plane and h be a nonconstant elliptic function. We show that if all zeros of f are multiple exept finitely many and T(r,h)=o{T(r,f)} as r tends to infinity, then f'=h has infinitely many…

Let a function $u(x,y)$ be harmonic in the domain $$ D\times V_r=D\times \{y\in \mathbb{R}^m: |y|<r\}\subset \mathbb{R}^n\times \mathbb{R}^m $$ and for each fixed point $x^0$ from some a set $E\subset D$, %which is not embedded in countable…

We determine completely the analytic functions $\varphi$ in the unit disk $\mathbb D$ such that for all (normalized) orientation-preserving harmonic mappings $f=h+\overline g$ produced by the shear construction with $h+g=\varphi$, the…