Remarks on Manifolds with Two-Sided Curvature Bounds

Abstract

We discuss folklore statements about distance functions in manifolds with two-sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.

Keywords

• distance functions
• cut locus
• subsets of positive reach
• harmonic coordinates
• alexandrov spaces
• 53c20
• 53c21
• 53c23