Sobolev mappings: Lipschitz density is not a bi-Lipschitz invariant of the target

被引：11
|
作者：
Hajlasz, Piotr [1 ]
机构：
[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
来源：
GEOMETRIC AND FUNCTIONAL ANALYSIS | 2007年 / 17卷 / 02期
基金：
美国国家科学基金会;
关键词：
Sobolev mappings; Lipschitz mappings; metric spaces; approximation;
D O I：
10.1007/s00039-007-0594-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study a question of density of Lipschitz mappings in the Sobolev class of mappings from a closed manifold into a singular space. The main result of the paper, Theorem 1.7, shows that if we change the metric in the target space to a bi-Lipschitz equivalent one, then the property of the density of Lipschitz mappings may be lost. Other main results in the paper are Theorems 1.2, 1.3, 1.6, 1.8.
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页码：435 / 467
页数：33
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