Delta-convex structure of the singular set of distance functions

被引：1

作者：

Miura, Tatsuya ^{[1
,3
]}

Tanaka, Minoru ^{[2
]}

机构：

[1] Tokyo Inst Technol, Dept Math, Meguro, Tokyo, Japan

[2] Tokai Univ, Sch Sci, Dept Math, Hiratsuka, Kanagawa, Japan

[3] Tokyo Inst Technol, Dept Math, Meguro, Tokyo 1528511, Japan

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2024年 / 77卷 / 09期

关键词：

CUT LOCUS; CLOSED SUBSETS; BOUNDARY; APPROXIMATION; PROPERTY; DOMAIN;

D O I：

10.1002/cpa.22195

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：3631 / 3669

页数：39

共 69 条

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