Apollonian isometries of planar domains are Möbius mappings

DOI10.1007/BF02922194zbMath1081.30039OpenAlexW1963856697MaRDI QIDQ2577088

Zair Ibragimov, Peter A. Hästö

Publication date: 3 January 2006

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02922194

zbMATH Keywords

Apollonian metricisometry.

Mathematics Subject Classification ID

General theory of conformal mappings (30C35) Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45)

Related Items (7)

Geometric characterizations of symmetric maps in the complex plane ⋮ Isometries for the modulus metric in higher dimensions are conformal mappings ⋮ Geometry of the Cassinian metric and its inner metric ⋮ Revisiting the foundations of Barbilian's metrization procedure ⋮ Isometries of relative metrics ⋮ Möbius invariant Cassinian metric ⋮ Apollonian isometries of planar domains are Möbius mappings

Cites Work

• A new weighted metric: the relative metric. II
• Barbilian spaces: the history of a geometric idea
• The quasihyperbolic metric and associated estimates on the hyperbolic metric
• Quasiconformally homogeneous domains
• A canonical metric for Möbius structures and its applications
• The Apollonian inner metric
• The Apollonian metric: limits of the comparison and bilipschitz properties
• Conformality of the Apollonian metric
• Apollonian isometries of planar domains are Möbius mappings
• 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
• Barbilian geometry and the Poincare Model
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