Lipschitz spaces and harmonic mappings
David Kalaj

TL;DR
This paper extends the bi-Lipschitz property of quasiconformal harmonic mappings to non-convex Jordan domains with smooth boundaries, removing previous convexity restrictions.
Contribution
It proves that quasiconformal harmonic mappings between Jordan domains with smooth boundaries are bi-Lipschitz without requiring convexity.
Findings
Bi-Lipschitz property holds for non-convex domains
Extends previous results to more general boundary conditions
Maintains bi-Lipschitz continuity under relaxed assumptions
Abstract
In \cite{kamz} the author proved that every quasiconformal harmonic mapping between two Jordan domains with , , boundary is bi-Lipschitz, providing that the domain is convex. In this paper we avoid the restriction of convexity. More precisely we prove: any quasiconformal harmonic mapping between two Jordan domains , , with , boundary is bi-Lipschitz.
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Taxonomy
TopicsAnalytic and geometric function theory · Nonlinear Partial Differential Equations · Holomorphic and Operator Theory
