Sphericalization and flattening

Balogh, Zoltán; Buckley, Stephen

doi:10.1090/S1088-4173-05-00124-4

Sphericalization and flattening
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by Zoltán M. Balogh and Stephen M. Buckley

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

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

Published electronically: 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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