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

Ulrich Menne, Mario Santilli

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1185-1198
Number of pages14
JournalAnnali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume19
Issue number3
DOIs
Publication statusPublished - 2019

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics (miscellaneous)

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