This paper gives a new proof of the fact that a -dimensional normal current in is integer multiplicity rectifiable if and only if for every projection onto a -dimensional subspace, almost every slice of by is -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.
@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}, pages = {905--924}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 1}, number = {4}, year = {2002}, zbl = {1096.49022}, mrnumber = {1991007}, language = {en}, url = {archive.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, Série 5, Tome 1 (2002) no. 4, pp. 905-924. http://archive.numdam.org/item/ASNSP_2002_5_1_4_905_0/
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