Homeomorphisms of Finite Metric Distortion Between Riemannian Manifolds

被引：0
|
作者：
Elena Afanas’eva
Anatoly Golberg
机构：
[1] Institute of Applied Mathematics and Mechanics of the NAS of Ukraine,Department of Mathematics
[2] Holon Institute of Technology,undefined
来源：
Computational Methods and Function Theory | 2022年 / 22卷
关键词：
Riemannian manifolds; Finitely bi-Lipschitz homeomorphisms; Quasisymmetry; Quasiconformality; Finite metric distortion; Lower ; -homeomorphisms; Moduli of families of curves and surfaces; Boundary behavior of bi-Lipschitz homeomorphisms; Lusin (; )-property; Primary: 30L10; 58B20; Secondary: 30C65; 53B20;
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学科分类号：
摘要：
The theory of multidimensional quasiconformal mappings employs three main approaches: analytic, geometric (modulus) and metric ones. In this paper, we use the last approach and establish the relationship between homeomorphisms of finite metric distortion (FMD-homeomorphisms), finitely bi-Lipschitz, quasisymmetric and quasiconformal mappings on Riemannian manifolds. One of the main results shows that FMD-homeomorphisms are lower Q-homeomorphisms. As an application, there are obtained some sufficient conditions for boundary extensions of FMD-homeomorphisms. These conditions are illustrated by several examples of FMD-homeomorphisms.
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页码：755 / 780
页数：25
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