Locally Lipschitz contractibility of Alexandrov spaces and its applications

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.

References in corpus (1)

• Semiconcave functions in Alexandrov's geometry

Cited by in corpus (1)

• Lipschitz 1-connectedness for some solvable Lie groups