DISTORTION OF AREA AND DIMENSION UNDER QUASI-CONFORMAL MAPPINGS IN THE PLANE

被引：3

作者：

ASTALA, K

机构：

[1] Department of Mathematics, University of Helsinki, SF-00014 Helsinki

来源：

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 1993年 / 90卷 / 24期

关键词：

D O I：

10.1073/pnas.90.24.11958

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We find the exact estimates for the distortion of area and Hausdorff dimension under a K-quasiconformal mapping of the complex plane. This solves also the problem of finding the precise bound p(K) of the exponents p such that for each planar K-quasiconformal mapping f the Jacobian J(f) is locally p-integrable; it follows that p(K) = 2K/(K - 1). Further consequences include among others the regularity and removability results for quasiregular mappings and sharp estimates for the complex Hilbert transform.

引用

页码：11958 / 11959

页数：2

共 14 条

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