距离函数奇异集的三角凸结构

IF 4.3 3区材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

ACS Applied Electronic Materials Pub Date : 2024-03-07 DOI:10.1002/cpa.22195

Tatsuya Miura, Minoru Tanaka

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引用次数: 0

摘要

对于从任何完整芬斯勒流形的任何封闭子集出发的距离函数，我们证明奇异集等于△凸超曲面的可数联合，直到一个标度为二的例外集。此外，在维数二中，整个奇异集等于直到孤立点的△凸约旦弧的可数联盟。即使在标准欧几里得空间中，这些结果也是新的，而且从正则性的角度来看，这些结果是最优的。

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Delta-convex structure of the singular set of distance functions

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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来源期刊

ACS Applied Electronic Materials Multiple-

CiteScore

7.20

自引率

4.30%

发文量

567