English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

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

MPS-Authors
/persons/resource/persons4295

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

/persons/resource/persons144466

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

External Ressource
No external resources are shared
Fulltext (public)

1703.09561.pdf
(Preprint), 202KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Menne, U., & Santilli, M. (2019). A geometric second-order-rectifiable stratification for closed subsets of Euclidean space. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 19(3), 1185-1198. doi:10.2422/2036-2145.201703_021.


Cite as: http://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.