Geodesically complete spaces with an upper curvature bound

Abstract

We study geometric and topological properties of locally compact, geodesically complete spaces with an upper curvature bound. We control the size of singular subsets, discuss homotopical and measure-theoretic stratifications and regularity of the metric structure on a large part.

Bibliography enlarged, formulations improved, minor corrections

Cited by in corpus (1)

• A lower bound for the curvature integral under an upper curvature bound