Extension and convergence theorems for families of normal maps in several complex variables

Extension and Convergence Theorems for Families of Normal Maps in Several Complex Variables

Let H(X, Y ) ( C(X, Y ) ) represent the family of holomorphic (continuous) maps from a complex (topological) space X to a complex (topological) space Y , and let Y + = Y ∪{∞} be the Alexandroff one–point compactification of Y if Y is not compact, Y + = Y if Y is compact. We say that F ⊂ H(X, Y ) is uniformly normal if {f ◦ φ : f ∈ F , φ ∈ H(M,X)} is relatively compact in C(M,Y +) (with the comp...

Three Structure Theorems in Several Complex Variables by Reese Harvey

The purpose of this article is to describe three recent structure theorems in the theory of several complex variables and to point out a few of the many applications of these three theorems. In the first section we discuss a characterization of those currents (defined on an open subset of C) which correspond to integration over complex subvarieties. The second section is concerned with the stru...

Kernel Convergence and Biholomorphic Mappings in Several Complex Variables

We deal with kernel convergence of domains in Cn which are biholomorphically equivalent to the unit ball B. We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings on B, which satisfy a growth theorem, and the kernel convergence. Moreover, we obtain certain consequences of this equivalence in the study of Loewner chains and of starlike and co...

Convergence Theorems For Two Finite Families of Uniformly L-Lipschitzian Mappings

Extension theorems for vector valued maps

We revisit studies on extension of Lipschitz maps and obtain new results about extension of displacements of bounded strain tensors. These questions are of interest in elasticity theory, optimal designs, as well as in functional analysis. Résumé Nous discutons l’extension d’applications Lipschitziennes et donnons, entre autres, une nouvelle démonstration d’un théorème de Schönbeck. Puis nous ét...