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

被引：7

作者：

Menne, Ulrich ^{[1
,2
]}

Santilli, Mario ^{[3
]}

机构：

[1] Natl Taiwan Normal Univ, Dept Math, 88,Sect 4,Tingzhou Rd, Taipei 11677, Taiwan

[2] Natl Ctr Theoret Sci, Math Div, 1,Sect 4,Roosevelt Rd, Toipei City 10617, Taiwan

[3] Univ Augsburg, Inst Math, D-86135 Augsburg, Germany

来源：

ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE | 2019年 / 19卷 / 03期

关键词：

SETS;

D O I：

10.2422/2036-2145.201703_021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：1185 / 1198

页数：14

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