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arXiv · 2204.10449

Delta-convex structure of the singular set of distance functions

Tatsuya Miura·Minoru Tanaka
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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.

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Tatsuya Miura, Minoru Tanaka. 2022-04-22. Delta-convex structure of the singular set of distance functions. https://doi.org/10.1002/cpa.22195

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