Sobolev Mappings: Lipschitz Density is not a Bi-Lipschitz Invariant of the Target

被引：0
|
作者：
Piotr Hajłasz
机构：
[1] University of Pittsburgh,Department of Mathematics
来源：
GAFA Geometric And Functional Analysis | 2007年 / 17卷
关键词：
Sobolev mappings; Lipschitz mappings; metric spaces; approximation; Primary: 46E35;
D O I：
暂无
中图分类号：
学科分类号：
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.
引用
收藏
页码：435 / 467
页数：32
相关论文
共 50 条
  • [41] Sharp Lipschitz constant of bi-Lipschitz automorphism on Cantor set
    XIONG Ying1
    Science China Mathematics, 2009, (04) : 709 - 719
  • [42] Sharp Lipschitz constant of bi-Lipschitz automorphism on Cantor set
    Xiong Ying
    Wang LiSha
    Xi LiFeng
    SCIENCE IN CHINA SERIES A-MATHEMATICS, 2009, 52 (04): : 709 - 719
  • [43] On the Lipschitz Constant for a Nonisometric Bi-Lipschitz Transformation of a Cantor Set
    M. S. Lyapina
    Journal of Mathematical Sciences, 2004, 120 (2) : 1109 - 1116
  • [44] On the piecewise approximation of bi-Lipschitz curves
    Pratelli, Aldo
    Radici, Emanuela
    RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, 2017, 138 : 1 - 37
  • [45] Dimension bounds for invariant measures of bi-Lipschitz iterated function systems
    Anckar, Andreas
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 440 (02) : 853 - 864
  • [46] Bi-Lipschitz geometry of quasiconformal trees
    David, Guy C.
    Vellis, Vyron
    ILLINOIS JOURNAL OF MATHEMATICS, 2022, 66 (02) : 189 - 244
  • [47] On the Bi-Lipschitz Geometry of Lamplighter Graphs
    F. Baudier
    P. Motakis
    Th. Schlumprecht
    A. Zsák
    Discrete & Computational Geometry, 2021, 66 : 203 - 235
  • [48] On the Bi-Lipschitz Geometry of Lamplighter Graphs
    Baudier, F.
    Motakis, P.
    Schlumprecht, Th.
    Zsak, A.
    DISCRETE & COMPUTATIONAL GEOMETRY, 2021, 66 (01) : 203 - 235
  • [49] THE DIRECTIONAL DIMENSION OF SUBANALYTIC SETS IS INVARIANT UNDER BI-LIPSCHITZ HOMEOMORPHISMS
    Koike, Satoshi
    Paunescu, Laurentiu
    ANNALES DE L INSTITUT FOURIER, 2009, 59 (06) : 2445 - 2467
  • [50] Bi-Lipschitz Characterization of Space Curves
    Fernandes, Alexandre
    Jelonek, Zbigniew
    BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2023, 54 (03):
12345