Quasisymmetry and Quasihyperbolicity of Mappings on John Domains

TY - JOUR

T1 - Quasisymmetry and Quasihyperbolicity of Mappings on John Domains

AU - Huang, Manzi

AU - Rasila, Antti

AU - Wang, Xiantao

AU - Zhou, Qingshan

N1 - Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2023/6

Y1 - 2023/6

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

SN - 1617-9447

VL - 23

SP - 237

EP - 268

JO - Computational Methods and Function Theory

JF - Computational Methods and Function Theory

IS - 2

ER -