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Conformal Geometry and Dynamics

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Universal convexity for quasihyperbolic type metrics


Author: David A. Herron
Journal: Conform. Geom. Dyn. 20 (2016), 1-24
MSC (2010): Primary 53A30; Secondary 53C22, 51F99, 30C65, 30F45
DOI: https://doi.org/10.1090/ecgd/288
Published electronically: February 24, 2016
MathSciNet review: 3463280
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Abstract: We characterize the open sets in the sphere that are geodesically convex in any containing domain with respect to various conformal metrics.


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David A. Herron
Affiliation: Department of Mathematical Sciences, French Hall West, PO Box 210025, Cincinnati Ohio 45221-0025
Email: David.Herron@UC.edu

DOI: https://doi.org/10.1090/ecgd/288
Keywords: Geodesic convexity, quasihyperbolic metric, Ferrand metric, Kulkarni-Pinkall metric, conformal metrics
Received by editor(s): November 10, 2015
Received by editor(s) in revised form: June 23, 2016
Published electronically: February 24, 2016
Dedicated: Dedicated to Taft Professor David Minda on the occasion of his retirement.
Article copyright: © Copyright 2016 American Mathematical Society

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