General univalence criteria and quasiconformal extensions starting from Loewner chains theory

Abstract

The aim of this paper is to obtain general univalence conditions and quasiconformal extensions to Cn of holomorphic mappings defined on the Euclidian unit ball B. The asymptotical case of the quasiconformal extension results is also presented. We extend several results obtained by Hamada and Kohr(2011) in [15] to a more general case. In particular our results improve certain univalence criteria and quasiconformal extension results previously obtained by Pfaltzgraff [21], [22], Curt and Pascu [8], Curt [5], Hamada and Kohr [16], Curt and Kohr [6], [7] and R?ducanu [24]. As applications we present general forms of the n-dimensional version of the well-known univalence criterion due to Lewandowski [19] and its quasiconformal extension.