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

被引：0

作者：

Donohue, Christopher G. ^{[1
]}

机构：

[1] Syracuse Univ, Dept Math, 215 Carnegie, Syracuse, NY 13244 USA

来源：

COMPUTATIONAL METHODS AND FUNCTION THEORY | 2023年 / 23卷 / 04期

关键词：

Conformal map; Hyperbolic metric; Kulkarni-Pinkall metric;

D O I：

10.1007/s40315-022-00457-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 the minimum curvature radius of its boundary. Its proof is based on a Mobius invariant metric of hyperbolic type, introduced by Kulkarni and Pinkall (Math Z 216(1):89-129, 1994).

引用

页码：651 / 661

页数：11

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