The quasiconformal subinvariance property of John domains in \protect \IRⁿ and its application

2011/08/29 by M. Huang, Y. Li, Huang, M. +7
Mathematics · #30F45 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Primary: 30C65 #Secondary: 30C20 #math.CV #msc:30C20 #msc:30C65 #msc:30F45

paper · pdf · doi:10.48550/arxiv.1108.5550

61 pages, under revision for Mathematische. Annalen

openalex publication_date 2011/08/29 · arxiv created 2013/07/19 · arxiv updated 2013/07/22 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

The main aim of this paper is to give a complete solution to one of the open problems, raised by Heinonen from 1989, concerning the subinvariance of John domains under quasiconformal mappings in \IRⁿ. As application, the quasisymmetry of quasiconformal mappings is discussed.

Citations

• Quasisymmetric parametrizations of two-dimensional metric spheres
• Quasiconformal maps in metric spaces with controlled geometry

Related

• On quasisymmetry of quasiconformal mappings and its applications
• John disk and K-quasiconformal harmonic mappings
• On invariance of John domains under quasisymmetric mappings
• Quasihyperbolic geodesics in John domains in Rⁿ
• On the subinvariance of uniform domains in metric spaces