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Metric-minimizing surfaces revisited

Anton Petrunin and Stephan Stadler

Geometry & Topology 23 (2019) 3111–3139
Abstract

A surface that does not admit a length nonincreasing deformation is called metric-minimizing. We show that metric-minimizing surfaces in CAT(0) spaces are locally CAT(0) with respect to their length metrics.

Keywords
metric-minimizing surfaces, intrinsic metric
Mathematical Subject Classification 2010
Primary: 53C23, 53C43, 53C45
Secondary: 30L05
References
Publication
Received: 4 April 2018
Revised: 7 October 2018
Accepted: 16 March 2019
Published: 1 December 2019
Proposed: Dmitri Burago
Seconded: Bruce Kleiner, Tobias H Colding
Authors
Anton Petrunin
Department of Mathematics
Pennsylvania State University
University Park, PA
United States
Stephan Stadler
Mathematisches Institut der Universität München
München
Germany