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.
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页码：166 / 181
页数：16
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