Geodesics and curvature of Möbius invariant metrics

DOI10.1216/RMJ-2008-38-3-891zbMath1171.30015OpenAlexW1976240867MaRDI QIDQ1011039

David A. Herron, Zair Ibragimov, David Minda

Publication date: 7 April 2009

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmj-2008-38-3-891

zbMATH Keywords

quasi-hyperbolic metricFerrand metricKulkarni-Pinkall metricPoincaré hyperbolic metric

Mathematics Subject Classification ID

Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Differentials on Riemann surfaces (30F30) General theory of univalent and multivalent functions of one complex variable (30C55)

Related Items (13)

A metric that better approximates the hyperbolic metric ⋮ Renormalized volume and the volume of the convex core ⋮ Chordal Hausdorff convergence and quasihyperbolic distance ⋮ Triangular ratio metric under quasiconformal mappings in sector domains ⋮ Carathéodory density of the Hurwitz metric on plane domains ⋮ Isometries for the modulus metric in higher dimensions are conformal mappings ⋮ Möbius invariant metrics bilipschitz equivalent to the hyperbolic metric ⋮ Geometry of the Cassinian metric and its inner metric ⋮ On uniqueness and prolongation of geodesics and convexity of balls ⋮ Estimates for conformal metric ratios ⋮ Universal convexity for quasihyperbolic type metrics ⋮ Centerlines of regions in the sphere ⋮ Conformally invariant complete metrics

Cites Work

• Lower bounds for the hyperbolic metric in convex regions
• The quasihyperbolic metric and associated estimates on the hyperbolic metric
• A canonical metric for Möbius structures and its applications
• Estimates for conformal metric ratios
• On a Class of Conformal Metrics
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