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arXiv · 1703.09561

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

Ulrich Menne·Mario Santilli
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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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Ulrich Menne, Mario Santilli. 2017-03-28. A geometric second-order-rectifiable stratification for closed subsets of Euclidean space. https://doi.org/10.2422/2036-2145.201703_021

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