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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

Möbius invariant metrics bilipschitz equivalent to the hyperbolic metric


Authors: David A. Herron, William Ma and David Minda
Journal: Conform. Geom. Dyn. 12 (2008), 67-96
MSC (2000): Primary 30F45; Secondary :, 30C55, 30F30
Published electronically: June 10, 2008
MathSciNet review: 2410919
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Abstract: We study three Möbius invariant metrics, and three affine invariant analogs, all of which are bilipschitz equivalent to the Poincaré hyperbolic metric. We exhibit numerous illustrative examples.


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Additional Information

David A. Herron
Affiliation: Department of Mathematical Sciences, 839 Old Chemistry Building, P.O. Box 210025, Cincinnati, Ohio 45221-0025
Email: David.Herron@math.UC.edu

William Ma
Affiliation: School of Integrated Studies, Pennsylvania College of Technology, Williamsport, Pennsylvania 17701
Email: wma@pct.edu

David Minda
Affiliation: Department of Mathematics, University of Cincinnati, Cincinnati, Ohio 45221
Email: david.minda@math.uc.edu

DOI: http://dx.doi.org/10.1090/S1088-4173-08-00178-1
PII: S 1088-4173(08)00178-1
Keywords: M\"obius metrics, Poincar\'e hyperbolic metric, uniformly perfect
Received by editor(s): November 30, 2007
Published electronically: June 10, 2008
Additional Notes: The first and third authors were supported by the Charles Phelps Taft Research Center.
Dedicated: Dedicated to Roger Barnard on the occasion of his $65^{th}$ birthday.
Article copyright: © Copyright 2008 American Mathematical Society