Reconstruction of domains from their groups of quasiconformal autohomeomorphisms

Vladimir Goldshtein; Matatyahu Rubin

doi:10.1016/0926-2245(95)92846-W

Reconstruction of domains from their groups of quasiconformal autohomeomorphisms

Vladimir Goldshtein, Matatyahu Rubin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

For an open set U ⊆ Rⁿ, let QC(U) denote the group of all quasiconformal homeo morphism of U. The following is our first main result. Let U ⊆ R^m and V ⊆ Rⁿ be open, and suppose that τ is a group isomorphism between QC(U) and QC(V). Then there is a quasiconformal homeomorphism θ{symbol} from U onto V such that φ{symbol} induce τ. That is, for every -f ε{lunate} QC(U): τ(-) = θ{symbol} -to - to θ{symbol}^-1.

Original language	English
Pages (from-to)	205-218
Number of pages	14
Journal	Differential Geometry and its Applications
Volume	5
Issue number	3
DOIs	https://doi.org/10.1016/0926-2245(95)92846-W
State	Published - 1 Jan 1995

Keywords

Homeomorphism groups
Lipschitz
Sobolev spaces
reconstruction

ASJC Scopus subject areas

Analysis
Geometry and Topology
Computational Theory and Mathematics

Access to Document

10.1016/0926-2245(95)92846-W

Cite this

@article{e42f04483dc945c5bbfd541fdb3b9611,

title = "Reconstruction of domains from their groups of quasiconformal autohomeomorphisms",

abstract = "For an open set U ⊆ Rn, let QC(U) denote the group of all quasiconformal homeo morphism of U. The following is our first main result. Let U ⊆ Rm and V ⊆ Rn be open, and suppose that τ is a group isomorphism between QC(U) and QC(V). Then there is a quasiconformal homeomorphism θ{symbol} from U onto V such that φ{symbol} induce τ. That is, for every -f ε{lunate} QC(U): τ(-) = θ{symbol} -to - to θ{symbol}-1.",

keywords = "Homeomorphism groups, Lipschitz, Sobolev spaces, reconstruction",

author = "Vladimir Goldshtein and Matatyahu Rubin",

year = "1995",

month = jan,

day = "1",

doi = "10.1016/0926-2245(95)92846-W",

language = "English",

volume = "5",

pages = "205--218",

journal = "Differential Geometry and its Applications",

issn = "0926-2245",

publisher = "Elsevier B.V.",

number = "3",

}

TY - JOUR

T1 - Reconstruction of domains from their groups of quasiconformal autohomeomorphisms

AU - Goldshtein, Vladimir

AU - Rubin, Matatyahu

PY - 1995/1/1

Y1 - 1995/1/1

N2 - For an open set U ⊆ Rn, let QC(U) denote the group of all quasiconformal homeo morphism of U. The following is our first main result. Let U ⊆ Rm and V ⊆ Rn be open, and suppose that τ is a group isomorphism between QC(U) and QC(V). Then there is a quasiconformal homeomorphism θ{symbol} from U onto V such that φ{symbol} induce τ. That is, for every -f ε{lunate} QC(U): τ(-) = θ{symbol} -to - to θ{symbol}-1.

AB - For an open set U ⊆ Rn, let QC(U) denote the group of all quasiconformal homeo morphism of U. The following is our first main result. Let U ⊆ Rm and V ⊆ Rn be open, and suppose that τ is a group isomorphism between QC(U) and QC(V). Then there is a quasiconformal homeomorphism θ{symbol} from U onto V such that φ{symbol} induce τ. That is, for every -f ε{lunate} QC(U): τ(-) = θ{symbol} -to - to θ{symbol}-1.

KW - Homeomorphism groups

KW - Lipschitz

KW - Sobolev spaces

KW - reconstruction

UR - http://www.scopus.com/inward/record.url?scp=0010764758&partnerID=8YFLogxK

U2 - 10.1016/0926-2245(95)92846-W

DO - 10.1016/0926-2245(95)92846-W

M3 - Article

AN - SCOPUS:0010764758

SN - 0926-2245

VL - 5

SP - 205

EP - 218

JO - Differential Geometry and its Applications

JF - Differential Geometry and its Applications

IS - 3

ER -

Reconstruction of domains from their groups of quasiconformal autohomeomorphisms

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this