TY - JOUR
T1 - A geometric second-order-rectifiable stratification for closed subsets of Euclidean space
AU - Menne, Ulrich
AU - Santilli, Mario
N1 - Publisher Copyright:
© 2019 Scuola Normale Superiore. All rights reserved.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
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U2 - 10.2422/2036-2145.201703_021
DO - 10.2422/2036-2145.201703_021
M3 - Article
AN - SCOPUS:85076278172
SN - 0391-173X
VL - 19
SP - 1185
EP - 1198
JO - Annali della Scuola normale superiore di Pisa - Classe di scienze
JF - Annali della Scuola normale superiore di Pisa - Classe di scienze
IS - 3
ER -