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

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Menne,  Ulrich
Geometric Measure Theory, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Santilli,  Mario
Geometric Measure Theory, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1703.09561.pdf
(Preprint), 202KB

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Citation

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


Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-E1B4-2
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.