4 papers · 1 filter
A note on polyharmonic mappings
Daoud Bshouty, Stavros Evdoridis, Antti Rasila
In this paper we prove a Radó type result showing that there is no univalent polyharmonic mapping of the unit disk onto the whole complex plane. We also establish a connection betw…
Koebe and Caratheódory type boundary behavior results for harmonic mappings
Daoud Bshouty, Jiaolong Chen, Stavros Evdoridis +1
We study the behavior of the boundary function of a harmonic mapping from global and local points of view. Results related to the Koebe lemma are proved, as well as a generalizatio…
A Problem of Bombieri on Univalent Functions
Dov Aharonov, Daoud Bshouty
The famous Bieberbach Conjecture from 1916 on the coefficients of normalized univalent functions defined in the unit disk that was finally proved by de Branges some 70 years later,…
A solution to Sheil-Small's harmonic mapping problem for Jordan polygons
Daoud Bshouty, Erik Lundberg, Allen Weitsman
The problem of mapping the interior of a Jordan polygon univalently by the Poisson integral of a step function was posed by T. Sheil-Small (1989). We describe a simple solution usi…