The Apollonian inner metric and uniform domains
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Publication:2786305
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
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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