Topological mappings of finite area distortion

被引：6

作者：

Afanas'eva, Elena ^{[1
]}

Golberg, Anatoly ^{[2
]}

机构：

[1] NAS Ukraine, Inst Appl Math & Mech, 1 Dobrovolskogo St, UA-84100 Slavyansk, Ukraine

[2] Holon Inst Technol, Dept Math, 52 Golomb St,POB 305, IL-5810201 Holon, Israel

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2022年 / 12卷 / 02期

关键词：

Riemannian manifolds; Mappings of finite area distortion; Finitely bi-Lipschitz homeomorphisms; Quasisymmetry; Quasiconformality; Quasimobius mappings; Q-homeomorphisms; Moduli of families of curves and surfaces; Boundary behavior of FAD-homeomorphisms; Sobolev classes; Absolute continuity; MAPS; CONTINUITY; SPACES;

D O I：

10.1007/s13324-022-00666-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the interplay of mappings of finite area distortion (FAD) with finitely bi-Lipschitz mappings, ring and lower Q-homeomorphisms, and absolutely continuous homeomorphisms of the class AC(Lambda)(n,p) on Riemannian manifolds. Some additional relations to the hyper Q-homeomorphisms, eta-quasisymmetric and omega-quasimobius mappings are also established. As applications of the above results, we provide several extension conditions to the weakly flat and strongly accessible boundaries under FAD-homeomorphisms.

引用

页数：29

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[30] On Distortion Estimates of Mappings with the Poletsky Condition in Domains with Poincare Inequality [J].

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