Metric-minimizing surfaces revisited

Petrunin, Anton; Stadler, Stephan

doi:10.2140/gt.2019.23.3111

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ISSN (electronic): 1364-0380

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Metric-minimizing surfaces revisited

Anton Petrunin and Stephan Stadler

Geometry & Topology 23 (2019) 3111–3139

DOI: 10.2140/gt.2019.23.3111

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

Volume 23, issue 6 (2019)