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

共 50 条

[31] Determination of formal CR mappings by a finite jet [J].

Juhlin, Robert .

ADVANCES IN MATHEMATICS, 2009, 222 (05) :1611-1648

[32] Distortion and stability of the fixed point property for non-expansive mappings [J].

Dominguez Benavides, T. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (06) :3229-3234

[33] Distortion theorems for homeomorphic Sobolev mappings of integrable p-dilatations [J].

Afanas'eva, Elena ;

Golberg, Anatoly ;

Salimov, Ruslan .

STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2022, 67 (02) :403-420

[34] Lower semicontinuity of mappings with bounded (θ, 1)-weighted (p, q)-distortion [J].

Vodop'yanov, S. K. ;

Molchanova, A. O. .

SIBERIAN MATHEMATICAL JOURNAL, 2016, 57 (05) :778-787

[35] On topological properties of families of finite sets [J].

Pina, Claribet ;

Uzcategui, Carlos .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2012, 119 (05) :1066-1077

[36] Holder and Lipschitz Continuity in Orlicz-Sobolev Classes, Distortion and Harmonic Mappings [J].

Mateljevic, Miodrag ;

Salimov, Ruslan ;

Sevostyanov, Evgeny .

FILOMAT, 2022, 36 (16) :5359-5390

[37] Other new types of Mappings with Strongly Closed Graphs in Topological spaces via e-θ and δ-β-θ-open sets [J].

AL Jumaili, Alaa. M. F. ;

Abed, Majid Mohammed ;

Al-sharqi, Faisal Ghazi .

1ST INTERNATIONAL SCIENTIFIC CONFERENCE ON PURE SCIENCE (ISCPS2019), 2019, 1234

[38] Geodetic topological cycles in locally finite graphs [J].

Georgakopoulos, Agelos ;

Spruessel, Philipp .

ELECTRONIC JOURNAL OF COMBINATORICS, 2009, 16 (01)

[39] Dynamics of meromorphic mappings with small topological degree II: Energy and invariant measure [J].

Diller, Jeffrey ;

Dujardin, Romain ;

Guedj, Vincent .

COMMENTARII MATHEMATICI HELVETICI, 2011, 86 (02) :277-316

[40] On the Lp-distortion of finite quotients of amenable groups [J].

Romain Tessera .

Positivity, 2012, 16 :633-640

← 1 2 3 4 5 →