Bi-Lipschitz quasiconformal extensions
Katsuhiko Matsuzaki
TL;DR
This paper reviews various techniques for extending quasisymmetric homeomorphisms of the real line into bi-Lipschitz diffeomorphisms of the upper half-plane, focusing on hyperbolic metric considerations.
Contribution
It provides a comprehensive survey of methods for bi-Lipschitz extensions of quasisymmetric maps in hyperbolic geometry.
Findings
Multiple extension methods are compared and analyzed.
Conditions for bi-Lipschitz extension are identified.
Applications to hyperbolic geometry are discussed.
Abstract
We survey several methods of extending quasisymmetric homeomorphisms of the real line to bi-Lipschitz diffeomorphisms of the upper half-plane with respect to the hyperbolic metric.
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Taxonomy
TopicsAnalytic and geometric function theory · Geometric and Algebraic Topology · Mathematical Dynamics and Fractals