Sphericalization and flattening

Authors:
Zoltán M. Balogh and Stephen M. Buckley

Journal:
Conform. Geom. Dyn. **9** (2005), 76-101

MSC (2000):
Primary 30F45

DOI:
https://doi.org/10.1090/S1088-4173-05-00124-4

Published electronically:
November 29, 2005

MathSciNet review:
2179368

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S1088-4173-05-00124-4

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.