Delta-convex structure of the singular set of distance functions

Abstract: For the distance function from any closed subset of any complete Finsler manifold, we prove that the singular set is equal to a countable union of delta-convex hypersurfaces up to an exceptional set of codimension two. In addition, in dimension two, the whole singular set is equal to a countable union of delta-convex Jordan arcs up to isolated points. These results are new even in the standard Euclidean space and shown to be optimal in view of regularity.

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Geodesics in global differential geometry (53C22) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Hamilton-Jacobi equations (35F21)

This page was built for publication: Delta-convex structure of the singular set of distance functions

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6507807)