Duality of Moduli and Quasiconformal Mappings in Metric Spaces

被引：3
|
作者：
Jones, Rebekah [1 ]
Lahti, Panu [2 ]
机构：
[1] Univ Cincinatti, Cincinnati, OH 45221 USA
[2] Univ Augsburg, Augsburg, Germany
来源：
ANALYSIS AND GEOMETRY IN METRIC SPACES | 2020年 / 8卷 / 01期
基金：
美国国家科学基金会;
关键词：
quasiconformal mapping; modulus of a family of surfaces; finite perimeter; fine topology; Poincare inequality; EXTREMAL LENGTH; FINITE PERIMETER; FINE CONTINUITY; QUASICONFORMALITY; SETS;
D O I：
10.1515/agms-2020-0112
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove a duality relation for the moduli of the family of curves connecting two sets and the family of surfaces separating the sets, in the setting of a complete metric space equipped with a doubling measure and supporting a Poincare inequality. Then we apply this to show that quasiconformal mappings can be characterized by the fact that they quasi-preserve the modulus of certain families of surfaces.
引用
收藏
页码：166 / 181
页数：16
相关论文
共 50 条
  • [41] Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings
    Vodop'yanov, S. K.
    Evseev, N. A.
    [J]. SIBERIAN MATHEMATICAL JOURNAL, 2015, 56 (05) : 789 - 821
  • [42] Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings
    S. K. Vodop’yanov
    N. A. Evseev
    [J]. Siberian Mathematical Journal, 2015, 56 : 789 - 821
  • [43] Triangular Ratio Metric Under Quasiconformal Mappings in Sector Domains
    Rainio, Oona
    Vuorinen, Matti
    [J]. COMPUTATIONAL METHODS AND FUNCTION THEORY, 2023, 23 (02) : 269 - 293
  • [44] Triangular Ratio Metric Under Quasiconformal Mappings in Sector Domains
    Oona Rainio
    Matti Vuorinen
    [J]. Computational Methods and Function Theory, 2023, 23 : 269 - 293
  • [45] DUALITY IN SPACES OF LORCH ANALYTIC MAPPINGS
    Moraes, Luiza A.
    Pereira, Alex F.
    [J]. QUARTERLY JOURNAL OF MATHEMATICS, 2016, 67 (03): : 431 - 438
  • [46] EQUIVARIANT METRIC FOR SMOOTH MODULI SPACES
    CHO, YS
    [J]. TOPOLOGY AND ITS APPLICATIONS, 1995, 62 (01) : 77 - 85
  • [47] Bergman metric on Teichmuller spaces and moduli spaces of curves
    Yeung, Sai-Kee
    [J]. RECENT PROGRESS ON SOME PROBLEMS IN SEVERAL COMPLEX VARIABLES AND PARTIAL DIFFERENTIAL EQUATIONS, 2006, 400 : 203 - 217
  • [48] SYZ duality for parabolic Higgs moduli spaces
    Biswas, Indranil
    Dey, A.
    [J]. NUCLEAR PHYSICS B, 2012, 862 (01) : 327 - 340
  • [49] ON DISTORTION OF THE MODULI OF RINGS UNDER LOCALLY QUASICONFORMAL MAPPINGS IN R-n
    Graf, S. Yu.
    [J]. PROBLEMY ANALIZA-ISSUES OF ANALYSIS, 2015, 4 (02): : 32 - 44
  • [50] Topological Angles and Freely Quasiconformal Mappings in Real Banach Spaces
    Yang, Zhiqiang
    Zhou, Qingshan
    [J]. COMPUTATIONAL METHODS AND FUNCTION THEORY, 2023, 23 (02) : 347 - 368
12345