On the valence of some classes of harmonic maps

We give examples which (i) disprove a conjecture of Sheil-Small regarding the valence of harmonic mappings of the unit disc to bounded convex domains, and (ii) answer negatively a question of the author regarding the valence of harmonic mappings with polynomial analytic and co-analytic parts.

Saved in:
Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 1991-09, Vol.110 (2), p.313-325
Main Author: Lyzzaik, Abdallah
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We give examples which (i) disprove a conjecture of Sheil-Small regarding the valence of harmonic mappings of the unit disc to bounded convex domains, and (ii) answer negatively a question of the author regarding the valence of harmonic mappings with polynomial analytic and co-analytic parts.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004100070390