Locally Lipschitz contractibility of Alexandrov spaces and its applications

TL;DR

This paper proves that finite-dimensional Alexandrov spaces with a lower curvature bound are locally Lipschitz contractible, providing new conditions for solving the Plateau problem in such spaces.

Contribution

It establishes the local Lipschitz contractibility of Alexandrov spaces with curvature bounds, advancing understanding of their geometric and topological properties.

Findings

Finite-dimensional Alexandrov spaces are locally Lipschitz contractible.

Provides a sufficient condition for solving the Plateau problem in Alexandrov spaces.

Enhances tools for geometric analysis in spaces with curvature bounds.

Abstract

We prove that any finite dimensional Alexandrov space with a lower curvature bound is locally Lipschitz contractible. As applications, we obtain a sufficient condition for solving the Plateau problem in an Alexandrov space considered by Mese and Zulkowski.