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• W2112875569 abstract "We show that the nearest point retraction is a uniform quasi-isometry from the Thurston metric on a hyperbolic domain $${Omega subset{hat{mathbb C}}}$$ to the boundary Dome(Ω) of the convex hull of its complement. As a corollary, one obtains explicit bounds on the quasi-isometry constant of the nearest point retraction with respect to the Poincaré metric when Ω is uniformly perfect. We also establish Marden and Markovic’s conjecture that Ω is uniformly perfect if and only if the nearest point retraction is Lipschitz with respect to the Poincaré metric on Ω." @default.
• W2112875569 created "2016-06-24" @default.
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• W2112875569 date "2010-10-30" @default.
• W2112875569 modified "2023-10-12" @default.
• W2112875569 title "The Thurston Metric on Hyperbolic Domains and Boundaries of Convex Hulls" @default.
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• W2112875569 doi "https://doi.org/10.1007/s00039-010-0102-7" @default.
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