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

 

Sphericalization and flattening


Authors: Zoltán M. Balogh and Stephen M. Buckley
Journal: Conform. Geom. Dyn. 9 (2005), 76-101
MSC (2000): Primary 30F45
Published electronically: November 29, 2005
MathSciNet review: 2179368
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Abstract: The conformal deformations of flattening and sphericalization of length metric spaces are considered. These deformations are dual to each other if the space satisfies a simple quantitative connectivity property. Moreover, the quasihyperbolic metrics corresponding to the flat and the spherical metrics are bilipschitz equivalent if a weaker connectivity condition is satisfied.


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Additional Information

Zoltán M. Balogh
Affiliation: Departament Mathematik, Universität Bern, Sidlerstrasse 5, 3012, Bern, Schweiz
Email: zoltan@math-stat.unibe.ch

Stephen M. Buckley
Affiliation: Department of Mathematics, National University of Ireland, Maynooth, Co. Kildare, Ireland
Email: sbuckley@maths.nuim.ie

DOI: http://dx.doi.org/10.1090/S1088-4173-05-00124-4
PII: S 1088-4173(05)00124-4
Received by editor(s): October 26, 2004
Received by editor(s) in revised form: September 28, 2005
Published electronically: November 29, 2005
Additional Notes: This research was partially supported by the Swiss Nationalfond and Enterprise Ireland. It was partly conducted during a visit by the second author to the University of Bern; the hospitality of the Mathematics Department was much appreciated.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.