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Sphericalization and flattening

Author(s): Zoltán M. Balogh; Stephen M. Buckley
Journal: Conform. Geom. Dyn. 9 (2005), 76-101.
MSC (2000): Primary 30F45
Posted: November 29, 2005
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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: 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
Posted: 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.
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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