Metric-minimizing surfaces revisited

Anton Petrunin; Stephan Stadler

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.

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Anton Petrunin. Stephan Stadler. "Metric-minimizing surfaces revisited." Geom. Topol. 23 (6) 3111 - 3139, 2019. https://doi.org/10.2140/gt.2019.23.3111

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Received: 4 April 2018; Revised: 7 October 2018; Accepted: 16 March 2019; Published: 2019

First available in Project Euclid: 7 December 2019

zbMATH: 07142695

MathSciNet: MR4039186

Digital Object Identifier: 10.2140/gt.2019.23.3111

Subjects:

Primary: 53C23 , 53C43 , 53C45

Secondary: 30L05

Keywords: Intrinsic metric , metric-minimizing surfaces

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