Higher order rectifiability of measures via averaged discrete curvatures

  • Sławomir Kolasiński

    University of Warsaw, Poland

Abstract

We provide a sufficient geometric condition for to be countably rectifiable of class (using the terminology of Federer), where is a Radon measure having positive lower density and finite upper density almost everywhere. Our condition involves integrals of certain many-point interaction functions (discrete curvatures) which measure flatness of simplexes spanned by the parameters.

Cite this article

Sławomir Kolasiński, Higher order rectifiability of measures via averaged discrete curvatures. Rev. Mat. Iberoam. 33 (2017), no. 3, pp. 861–884

DOI 10.4171/RMI/958