Sphericalization and flattening
Balogh, Zoltán M. and Buckley, Stephen M. (2005) Sphericalization and flattening. Conformal Geometry and Dynamics. An Electronic Journal of the AMS, 9 . pp. 76-101. ISSN 1088-4173
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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