233 research outputs found
Minimal surfaces and Schwarz lemma
We prove a sharp Schwarz type inequality for the Weierstrass- Enneper
representation of the minimal surfaces. It states the following. If
is a conformal harmonic parameterization of a minimal
disk , where is the unit disk and , then
. If for some the previous inequality is equality,
then the surface is an affine disk, and is linear up to a M\"obius
transformation of the unit disk.Comment: 6 page
Lipschitz spaces and harmonic mappings
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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