A geometric second-order-rectifiable stratification for closed subsets of Euclidean space

Ulrich Menne, Mario Santilli

研究成果: 雜誌貢獻期刊論文同行評審

5 引文 斯高帕斯(Scopus)

摘要

Defining the m-th stratum of a closed subset of an n dimensional Euclidean space to consist of those points, where it can be touched by a ball from at least n - m linearly independent directions, we establish that the m-th stratum is second-order rectifiable of dimension m and a Borel set. This was known for convex sets, but is new even for sets of positive reach. The result is based on a sufficient condition of parametric type for second-order rectifiability.

原文英語
頁(從 - 到)1185-1198
頁數14
期刊Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
19
發行號3
DOIs
出版狀態已發佈 - 2019

ASJC Scopus subject areas

  • 理論電腦科學
  • 數學(雜項)

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