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

Menne, U., & Santilli, M. (submitted). A geometric second-order-rectifiable stratification for closed subsets of Euclidean space.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-E1B4-2 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-F776-3
Genre: Paper

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1703.09561.pdf (Preprint), 202KB
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 Creators:
Menne, Ulrich1, Author              
Santilli, Mario1, Author              
Affiliations:
1Geometric Measure Theory, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_1753352              

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Free keywords: Mathematics, Classical Analysis and ODEs, math.CA,Mathematics, Differential Geometry, math.DG,
 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 new criterion for second-order rectifiability.

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 Dates: 2017-03-282017-04-092017
 Publication Status: Submitted
 Pages: 13 pages. v2: corrected a typographical error in the introduction, and updated the affiliation of the first author
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 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1703.09561
URI: http://arxiv.org/abs/1703.09561
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