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Delta‐convex structure of the singular set of distance functions.
- Source :
-
Communications on Pure & Applied Mathematics . Sep2024, Vol. 77 Issue 9, p3631-3669. 39p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SET functions
*HYPERSURFACES
Subjects
Details
- Language :
- English
- ISSN :
- 00103640
- Volume :
- 77
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Communications on Pure & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 178355544
- Full Text :
- https://doi.org/10.1002/cpa.22195