Invertible harmonic mappings beyond Kneser theorem and quasiconformal harmonic mappings
David Kalaj
TL;DR
This paper extends classical harmonic mapping theorems to broader conditions, including non-convex domains and Lipschitz boundary data, with applications to quasiconformal harmonic mappings.
Contribution
It generalizes the Rado-Choquet-Kneser theorem to non-convex domains and Lipschitz boundary conditions, expanding the scope of harmonic mapping theory.
Findings
Extended the Rado-Choquet-Kneser theorem beyond convex domains.
Provided new results for quasiconformal harmonic mappings.
Demonstrated applications to mappings between Jordan domains.
Abstract
In this paper we extend Rado-Choquet-Kneser theorem for the mappings with Lipschitz boundary data and essentially positive Jacobian at the boundary, without restriction on the convexity of image domain. It is an extension of a recent result of Alessandrini and Nesi \cite{ale}. Some applications for the family of quasiconformal harmonic mappings between Jordan domains are given.
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