The Apollonian inner metric and uniform domains

DOI10.1002/mana.200710092zbMath1201.30054OpenAlexW2033319791MaRDI QIDQ2786305

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Publication date: 21 September 2010

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.200710092

zbMATH Keywords

quasihyperbolic metricuniform domaininner metricapollonian metric

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45)

Related Items (4)

Uniform domains, John domains and quasi-isotropic domains ⋮ A note on Väisälä's problem concerning free quasiconformal mappings ⋮ Equivalence of the Apollonian and its inner metric ⋮ Local convexity properties of balls in Apollonian and Seittenranta’s metrics

Cites Work

• The Apollonian metric: quasi-isotropy and Seittenranta's metric
• Convex bodies of constant width and the Apollonian metric
• Conformal invariants and quasiregular mappings
• Uniform domains and the quasi-hyperbolic metric
• Quasiconformally homogeneous domains
• Hyperbolic geometry and disks
• The Apollonian inner metric
• The Apollonian metric: limits of the comparison and bilipschitz properties
• Uniform domains and the ubiquitous quasidisk
• Conformality of the Apollonian metric
• Definitions for uniform domains
• Injectivity theorems in plane and space
• Möbius-invariant metrics
• Thick sets and quasisymmetric maps
• An Upper Bound for the Hyperbolic Metric of a Convex Domain
• On the apollonian metric of domains in
• Isometries of the Half-Apollonian Metric
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