Quasiconformal harmonic mappings between Euclidean surfaces

被引：0
作者：
Kalaj, David [1 ]
机构：
[1] Univ Montenegro, Fac Nat Sci & Math, Cetinjski Put Bb, Podgorica 81000, Montenegro
来源：
MONATSHEFTE FUR MATHEMATIK | 2012年 / 167卷 / 02期
关键词：
Harmonic mappings; Quasiconformal mappings; Poisson integral; Minimal surfaces; Regular surfaces; UNIVERSAL TEICHMULLER SPACE; CONSTANT MEAN-CURVATURE; MINIMAL SURFACES; BOUNDARY-BEHAVIOR; SELF-MAPPINGS; UNIT DISK; MAPS; DIFFEOMORPHISMS; DOMAINS; PLANE;
D O I：
10.1007/s00605-011-0355-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The conformal deformations are contained in two classes of mappings quasiconformal and harmonic mappings. In this paper we consider the intersection of these classes. We show that, every K quasiconformal harmonic mapping between surfaces with boundary is a Lipschitz mapping. This extends some recent results of several authors where the same problem has been considered for plane domains. As an application it is given an explicit Lipschitz constant of normalized isothermal coordinates of a disk-type minimal surface in terms of boundary curve only. It seems that this kind of estimates are new for conformal mappings of the unit disk onto a Jordan domain as well.
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页码：205 / 229
页数：25
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