Hopf Differentials and Smoothing Sobolev Homeomorphisms

被引：40

作者：

Iwaniec, Tadeusz ^{[1
,2
]}

Kovalev, Leonid V. ^{[1
]}

Onninen, Jani ^{[1
]}

机构：

[1] Syracuse Univ, Dept Math, Syracuse, NY 13244 USA

[2] Univ Helsinki, Dept Math & Stat, FIN-00014 Helsinki, Finland

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2012年 / 2012卷 / 14期

基金：

美国国家科学基金会; 芬兰科学院;

关键词：

QUASI-CONFORMAL MAPPINGS; REGULARITY; APPROXIMATION;

D O I：

10.1093/imrn/rnr144

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that planar homeomorphisms can be approximated by diffeomorphisms in the Sobolev space W-1,W-2 and in the Royden algebra. As an application, we show that every discrete and open planar mapping with a holomorphic Hopf differential is harmonic.

引用

页码：3256 / 3277

页数：22

共 28 条

[1]

[Anonymous], 1977, Grundlagen der mathematischen Wissenschaften

[2]

[Anonymous], 2009, Princeton Mathematical Series

[3]

[Anonymous], 1992, GRUNDLEHREN MATH WIS

[4]

[Anonymous], 1991, 2 DIMENSIONAL GEOMET

[5]

[Anonymous], 1983, CBMS Regional Conference Series in Math., vol. 50, Amer. Math. Soc

[6]

Ball J.M., 1999, FDN COMPUT MATH, V284, P1

[7] GLOBAL INVERTIBILITY OF SOBOLEV FUNCTIONS AND THE INTERPENETRATION OF MATTER [J].

BALL, JM .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1981, 88 :315-328

[8]

Bellido JC, 2011, HOUSTON J MATH, V37, P449

[9]

Dierkes U, 1992, Minimal Surfaces, VI

[10]

Duren P., 2004, CAMBRIDGE TRACTS MAT, V156

← 1 2 3 →