Uniformly perfect domains and convex hulls

Martin Bridgeman; Richard Canary

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arXiv · 1110.2114

Uniformly perfect domains and convex hulls

Martin Bridgeman·Richard Canary

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Abstract

Given a hyperbolic domain, the nearest point retraction is a conformally natural homotopy equivalence from the domain to the boundary of the convex core of its complement. Marden and Markovic showed that if the domain is uniformly perfect, then there exists a conformally natural quasiconformal map which admits a bounded homotopy to the nearest point retraction. We obtain an explicit upper bound on the quasiconformal dilatation which depends only on the injectivity radius of the domain.

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Martin Bridgeman, Richard Canary. 2012-08-01. Uniformly perfect domains and convex hulls. https://arxiv.org/abs/1110.2114

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