Volume 23, issue 6 (2019)

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Metric-minimizing surfaces revisited

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 $CAT\left(0\right)$ spaces are locally $CAT\left(0\right)$ with respect to their length metrics.

Keywords
metric-minimizing surfaces, intrinsic metric
Mathematical Subject Classification 2010
Primary: 53C23, 53C43, 53C45
Secondary: 30L05