Higher order rectifiability of measures via averaged discrete curvatures

• Sławomir Kolasiński ^[1]
  1. [1] University of Warsaw

     University of Warsaw

     Warszawa, Polonia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 33, Nº 3, 2017 (Ejemplar dedicado a: Yves Meyer), págs. 861-884
• Idioma: inglés
• DOI: 10.4171/RMI/958
• Texto completo no disponible (Saber más ...)
• Resumen

  • We provide a sufficient geometric condition for Rn to be countably (μ,m) rectifiable of class C1,α (using the terminology of Federer), where μ is a Radon measure having positive lower density and finite upper density μ almost everywhere. Our condition involves integrals of certain many-point interaction functions (discrete curvatures) which measure flatness of simplexes spanned by the parameters.