Locally Lipschitz contractibility of Alexandrov spaces and its applications

Ayato Mitsuishi and Takao Yamaguchi

Vol. 270 (2014), No. 2, 393–421

DOI: 10.2140/pjm.2014.270.393

Abstract

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

Keywords

Alexandrov space, Lipschitz contractibility

Mathematical Subject Classification 2010

Primary: 53C20, 53C21, 53C23

Milestones

Received: 17 February 2013

Revised: 21 August 2013

Accepted: 21 December 2013

Published: 22 August 2014