Abstract
AbstractFor 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.
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