Uniformity from Gromov hyperbolicity

zbMath1189.30055MaRDI QIDQ2654667

David A. Herron, Nageswari Shanmugalingam, Xiangdong Xie

Publication date: 20 January 2010

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ijm/1258554351

zbMATH Keywords

hyperbolic domainquasiconformal structurequasi-Möbius homeomorphism

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (17)

Weakly quasisymmetric maps and uniform spaces ⋮ Gromov hyperbolicity in the free quasiworld. I ⋮ Best constants for metric space inversion inequalities ⋮ Sphericalization and flattening in quasi-metric measure spaces ⋮ Extension and trace results for doubling metric measure spaces and their hyperbolic fillings ⋮ Constructing uniform spaces ⋮ Relatively quasimöbius mappings in Banach spaces ⋮ Unnamed Item ⋮ The spherical boundary and volume growth ⋮ Distortion of quasiconformal maps in terms of the quasihyperbolic metric ⋮ Teichmüller's problem for Gromov hyperbolic domains ⋮ Semisolidity and locally weak quasisymmetry of homeomorphisms in metric spaces ⋮ Geometric analysis on Cantor sets and trees ⋮ Bounded geometry and \(p\)-harmonic functions under uniformization and hyperbolization ⋮ Sphericalizations and applications in Gromov hyperbolic spaces ⋮ Conformal transformation of uniform domains under weights that depend on distance to the boundary ⋮ SPHERICALIZATION AND FLATTENING PRESERVE UNIFORM DOMAINS IN NONLOCALLY COMPACT METRIC SPACES

Cites Work

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• Quasiconformally homogeneous domains
• Rigidity for quasi-Möbius group actions
• Embeddings of Gromov hyperbolic spaces
• Uniform domains and the ubiquitous quasidisk
• Uniform domains and quasiconformal mappings on the Heisenberg group
• Geometric implications of the Poincaré inequality
• Gromov hyperbolic spaces
• POTENTIAL-THEORETIC CHARACTERIZATIONS OF NONSMOOTH DOMAINS
• Un Groupe Hyperbolique Est Déterminé Par Son Bord

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