Equivalence of the Apollonian and its inner metric

DOI10.1155/2010/191858zbMath1194.30047OpenAlexW2031044005WikidataQ58651707 ScholiaQ58651707MaRDI QIDQ978981

Swadesh Kumar Sahoo, Saminathan Ponnusamy, Peter A. Hästö

Publication date: 25 June 2010

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2010/191858

zbMATH Keywords

inner metricApollonian metric

Mathematics Subject Classification ID

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

Cites Work

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• The Apollonian metric: quasi-isotropy and Seittenranta's metric
• Convex bodies of constant width and the Apollonian metric
• Barbilian spaces: the history of a geometric idea
• Conformal invariants and quasiregular mappings
• Uniform domains and the quasi-hyperbolic metric
• Quasiconformal mappings and extendability of functions in Sobolev spaces
• Conformal geometry and quasiregular mappings
• Quasiconformally homogeneous domains
• 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
• The Apollonian inner metric and uniform domains
• Injectivity theorems in plane and space
• Möbius-invariant metrics
• An Upper Bound for the Hyperbolic Metric of a Convex Domain
• The Apollonian Metric: The Comparison Property, Bilipschitz Mappings and Thick Sets
• Barbilian geometry and the Poincare Model

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