A new proof of the rectifiable slices theorem

• Robert L. Jerrard ^[1]
  1. [1] University of Illinois
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 1, Nº 4, 2002, págs. 905-924
• Idioma: inglés
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• Resumen

  • This paper gives a new proof of the fact that a $k$-dimensional normal current $T$ in $\mathbb{R}^m$ is integer multiplicity rectifiable if and only if for every projection $P$ onto a $k$-dimensional subspace, almost every slice of $T$ by $P$ is $0$-dimensional integer multiplicity rectifiable, in other words, a sum of Dirac masses with integer weights. This is a special case of the Rectifiable Slices Theorem, which was first proved a few years ago by B. White.