Vol. 270, No. 2, 2014

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Locally Lipschitz contractibility of Alexandrov spaces and its applications

Ayato Mitsuishi and Takao Yamaguchi

Vol. 270 (2014), No. 2, 393–421
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
Authors
Ayato Mitsuishi
Mathematical Institute
Tohoku University
6-3, Aoba, Aramaki, Aoba-ku
Sendai 980-8578
Japan
Takao Yamaguchi
Department of Mathematics
Kyoto University
Kitashirakawa
Kyoto 606-8502
Japan