Metric minimizing surfaces revisited

TL;DR

This paper revisits metric minimizing surfaces and proves that in CAT(0) spaces, such surfaces are locally CAT(0) with respect to their intrinsic metric, deepening understanding of their geometric properties.

Contribution

It establishes that metric minimizing surfaces in CAT(0) spaces are locally CAT(0), providing new insights into their geometric structure.

Findings

Metric minimizing surfaces in CAT(0) spaces are locally CAT(0).

The intrinsic metric of these surfaces inherits CAT(0) properties.

Enhances understanding of surface behavior in non-positive curvature spaces.

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.