A new proof of the rectifiable slices theorem

Jerrard, Robert L.

Jerrard, Robert L.

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 4, p. 905-924

Abstract

This paper gives a new proof of the fact that a $k$ -dimensional normal current $T$ in $ℝ^{m}$ 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.

MR 1991007 | Zbl 1096.49022

Classification: 49Q15

@article{ASNSP_2002_5_1_4_905_0,
     author = {Jerrard, Robert L.},
     title = {A new proof of the rectifiable slices theorem},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {4},
     year = {2002},
     pages = {905-924},
     zbl = {1096.49022},
     mrnumber = {1991007},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2002_5_1_4_905_0}
}

Jerrard, Robert L. A new proof of the rectifiable slices theorem. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 4, pp. 905-924. http://www.numdam.org/item/ASNSP_2002_5_1_4_905_0/

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