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Petrunin, Anton; Stadler, Stephan (2019): Metric-minimizing surfaces revisited. In: Geometry & Topology, Vol. 23, No. 6: pp. 3111-3139
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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.