Mappings with convex potentials and the quasiconformal Jacobian problem

被引：21
|
作者：
Kovalev, Leonid V.
Maldonado, Diego
机构：
[1] Washington Univ, Dept Math, St Louis, MO 63130 USA
[2] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
来源：
ILLINOIS JOURNAL OF MATHEMATICS | 2005年 / 49卷 / 04期
关键词：
D O I：
10.1215/ijm/1258138126
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper concerns convex functions that arise as potentials of quasiconformal mappings. Several equivalent definitions for such functions are given. We use them to construct quasiconformal mappings whose Jacobian determinants are singular on a prescribed set of Hausdorff dimension less than 1.
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页码：1039 / 1060
页数：22
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