Uniform Lipschitz extension in bounded curvature

TL;DR

This paper establishes a uniform extension theorem for contracting maps on subsets of Hadamard manifolds with curvature constraints, advancing the understanding of Lipschitz extensions in curved geometric spaces.

Contribution

It introduces a new uniform extension result for Lipschitz maps in Hadamard manifolds with bounded curvature, expanding the theory of Lipschitz extensions in geometric analysis.

Findings

Proves a uniform Lipschitz extension theorem for Hadamard manifolds.

Establishes bounds for extensions under curvature constraints.

Enhances understanding of Lipschitz maps in curved spaces.

Abstract

We prove a uniform extension result for contracting maps defined on subsets of Hadamard manifolds subject to curvature bounds.