Metric minimizing surfaces revisited

Abstract

A surface which 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 intrinsic metric.

References in corpus (2)

• Area minimizing discs in metric spaces
• Monotonicity of saddle maps

Cited by in corpus (2)

• Two-dimensional metric spaces with curvature bounded above I
• Isoperimetric inequalities vs. upper curvature bounds