Quasisymmetry and Quasihyperbolicity of Mappings on John Domains

Manzi Huang; Antti Rasila; Xiantao Wang; Qingshan Zhou

doi:10.1007/s40315-022-00440-w

Quasisymmetry and Quasihyperbolicity of Mappings on John Domains

Manzi Huang, Antti Rasila, Xiantao Wang^*, Qingshan Zhou

^*Corresponding author for this work

Mathematics with Computer Science

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

Abstract

Suppose that G is a proper subdomain of Rⁿ, f: G→ Y is a homeomorphism with a continuous extension to the inner boundary of G, i.e., the boundary of G with respect to the corresponding inner metric, where (Y, d^′) stands for a locally compact, non-complete and rectifiably connected metric space, and that G^′= f(G) is uniform in Y. The purpose of this paper is to prove that G is a John domain if f is M-quasihyperbolic in G and the restriction of f on the inner boundary of G is η-quasisymmetric with respect to the inner metric.

Original language	English
Journal	Computational Methods and Function Theory
DOIs	https://doi.org/10.1007/s40315-022-00440-w
State	Accepted/In press - 2022

Keywords

Characterization
Gromov hyperbolicity
Inner uniformity
Quasisymmetry
Uniformity

Access to Document

10.1007/s40315-022-00440-w

Cite this

@article{9d63837e58ed4267bcd845b47c3e1eef,

title = "Quasisymmetry and Quasihyperbolicity of Mappings on John Domains",

abstract = "Suppose that G is a proper subdomain of Rn, f: G→ Y is a homeomorphism with a continuous extension to the inner boundary of G, i.e., the boundary of G with respect to the corresponding inner metric, where (Y, d′) stands for a locally compact, non-complete and rectifiably connected metric space, and that G′= f(G) is uniform in Y. The purpose of this paper is to prove that G is a John domain if f is M-quasihyperbolic in G and the restriction of f on the inner boundary of G is η-quasisymmetric with respect to the inner metric.",

keywords = "Characterization, Gromov hyperbolicity, Inner uniformity, Quasisymmetry, Uniformity",

author = "Manzi Huang and Antti Rasila and Xiantao Wang and Qingshan Zhou",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2022",

doi = "10.1007/s40315-022-00440-w",

language = "英语",

journal = "Computational Methods and Function Theory",

issn = "1617-9447",

publisher = "Springer Verlag",

}

TY - JOUR

T1 - Quasisymmetry and Quasihyperbolicity of Mappings on John Domains

AU - Huang, Manzi

AU - Rasila, Antti

AU - Wang, Xiantao

AU - Zhou, Qingshan

PY - 2022

Y1 - 2022

N2 - Suppose that G is a proper subdomain of Rn, f: G→ Y is a homeomorphism with a continuous extension to the inner boundary of G, i.e., the boundary of G with respect to the corresponding inner metric, where (Y, d′) stands for a locally compact, non-complete and rectifiably connected metric space, and that G′= f(G) is uniform in Y. The purpose of this paper is to prove that G is a John domain if f is M-quasihyperbolic in G and the restriction of f on the inner boundary of G is η-quasisymmetric with respect to the inner metric.

AB - Suppose that G is a proper subdomain of Rn, f: G→ Y is a homeomorphism with a continuous extension to the inner boundary of G, i.e., the boundary of G with respect to the corresponding inner metric, where (Y, d′) stands for a locally compact, non-complete and rectifiably connected metric space, and that G′= f(G) is uniform in Y. The purpose of this paper is to prove that G is a John domain if f is M-quasihyperbolic in G and the restriction of f on the inner boundary of G is η-quasisymmetric with respect to the inner metric.

KW - Characterization

KW - Gromov hyperbolicity

KW - Inner uniformity

KW - Quasisymmetry

KW - Uniformity

UR - http://www.scopus.com/inward/record.url?scp=85127383439&partnerID=8YFLogxK

U2 - 10.1007/s40315-022-00440-w

DO - 10.1007/s40315-022-00440-w

M3 - 文章

AN - SCOPUS:85127383439

JO - Computational Methods and Function Theory

JF - Computational Methods and Function Theory

SN - 1617-9447

ER -

Quasisymmetry and Quasihyperbolicity of Mappings on John Domains

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this