Calculus of Variations and Geometric Measure Theory
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U. Menne - M. Santilli

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

created by santilli on 21 Jul 2020


Published Paper

Inserted: 21 jul 2020
Last Updated: 21 jul 2020

Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)
Volume: 19(3) (2019)
Year: 2017
Doi: 10.2422/2036-2145.201703_021

ArXiv: 1703.09561 PDF


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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