Remarks on manifolds with two-sided curvature bounds (Q1983821)

The authors discuss results about the distance function and the cut locus of a closed subset of a smooth Riemannian manifold without assuming completeness. They show that these results also hold for manifolds with a two-sided curvature bound in the sense of Alexandrov. For this class of manifolds they investigate the regularity of harmonic functions in distance coordinates and show that \(C^{1,1}\)-submanifolds have positive reach.