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arXiv · 2106.03808

Lipschitz Estimates for Conformal Maps from the Unit Disk to Convex Domains

Christopher G. Donohue
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Abstract

We obtain an explicit uniform upper bound for the derivative of a conformal mapping of the unit disk onto a convex domain. This estimate depends only on the outer and inner radii of the domain, and on a curvature radius of its boundary. Its proof is based on a M\"obius invariant metric of hyperbolic type, introduced by Kulkarni and Pinkall in 1994.

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Christopher G. Donohue. 2021-06-07. Lipschitz Estimates for Conformal Maps from the Unit Disk to Convex Domains. https://arxiv.org/abs/2106.03808

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