Quasihomeomorphisms and univalent harmonic mappings onto punctured bounded convex domains

Abdallah Lyzzaik

Vol. 200 (2001), No. 1, 159–190

DOI: 10.2140/pjm.2001.200.159

Abstract

This paper deals with univalent harmonic mappings of annuli onto punctured bounded convex domains. Several aspects of these mappings are investigated; in particular, boundary functions, existence and uniquenss questions, and the geometry of their analytic and (co-analytic) parts. The paper also considers univalence criteria for Dirichlet solutions in annuli of boundary functions that are a generalized type of homeomorphisms, called quasihomeomorphisms, on one boundary component and constants on the other.

Milestones

Received: 15 October 1999

Published: 1 September 2001