A geometric second-order-rectifiable stratification for closed subsets of Euclidean space
Classical Analysis and ODEs
2019-09-27 v2 Differential Geometry
Abstract
Defining the -th stratum of a closed subset of an dimensional Euclidean space to consist of those points, where it can be touched by a ball from at least linearly independent directions, we establish that the -th stratum is second-order rectifiable of dimension 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 new criterion for second-order rectifiability.
Keywords
Cite
@article{arxiv.1703.09561,
title = {A geometric second-order-rectifiable stratification for closed subsets of Euclidean space},
author = {Ulrich Menne and Mario Santilli},
journal= {arXiv preprint arXiv:1703.09561},
year = {2019}
}
Comments
13 pages. v2: corrected a typographical error in the introduction, and updated the affiliation of the first author