CONFORMALITY OF QUASICONFORMAL MAPPINGS AT A POINT, REVISITED

被引：5

作者：

Shishikura, Mitsuhiro ^{[1
]}

机构：

[1] Kyoto Univ, Dept Math, Kyoto 6068502, Japan

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2018年 / 43卷

关键词：

Quasiconformal mapping; BEHAVIOR;

D O I：

10.5186/aasfm.2018.4359

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a new and simple proof of Teichmfiller-Wittich-Belinskit's and Gutlyanskii-Martio's theorems on the conformality of quasiconformal mappings at a given point. Known proofs gave separate estimates for the radial and angular variations, but our proof unifies them using Grotzsch-type inequality for the variation of cross-ratio of four points on the Riemann sphere. We also give a sufficient condition for C1+alpha-conformality.

引用

页码：981 / 990

页数：10

共 16 条

[1]

Ahlfors L., 2006, U LECT SER, V38

[2]

Ahlfors Lars V., 1973, Conformal Invariants: Topics in Geometric Function Theory

[3]

[Anonymous], 1973, QUASICONFORMAL MAPPI, DOI DOI 10.1007/978-3-642-65513-5

[4]

BELINSKII P. P., 1954, L'vov Gos. Univ. Uchen. Zap. Ser. Meh. Mat., V6, P58

[5]

Belinskii PP, 1974, General Properties of Quasiconformal Maps

[6]

Brakalova M., 1994, KODAI MATH J, V17, P201, DOI [10.2996/kmj/1138039960, DOI 10.2996/KMJ/1138039960]

[7]

Drasin D., 1986, RESULTS MATH, V10, P54

[8]

GARDINER F. P., 2000, Mathematical Surveys and Monographs, V76

[9] Conformality of a quasiconformal mapping at a point [J].

Gutlyanskii, V ;

Martio, O .

JOURNAL D ANALYSE MATHEMATIQUE, 2003, 91 (1) :179-192

[10]

Hubbard J, 2009, J AM MATH SOC, V22, P77

← 1 2 →