A new proof of the rectifiable slices theorem

Robert L. Jerrard

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 4, page 905-924
  • ISSN: 0391-173X

Abstract

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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.

How to cite

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Jerrard, Robert L.. "A new proof of the rectifiable slices theorem." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.4 (2002): 905-924. <http://eudml.org/doc/84491>.

@article{Jerrard2002,
abstract = {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.},
author = {Jerrard, Robert L.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {normal currents},
language = {eng},
number = {4},
pages = {905-924},
publisher = {Scuola normale superiore},
title = {A new proof of the rectifiable slices theorem},
url = {http://eudml.org/doc/84491},
volume = {1},
year = {2002},
}

TY - JOUR
AU - Jerrard, Robert L.
TI - A new proof of the rectifiable slices theorem
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2002
PB - Scuola normale superiore
VL - 1
IS - 4
SP - 905
EP - 924
AB - 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.
LA - eng
KW - normal currents
UR - http://eudml.org/doc/84491
ER -

References

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  9. [9] R. L. Jerrard – H. M. Soner, Rectifiability of the distributional Jacobian for a class of functions, C.R. Acad. Sci. Paris, Série I, 329 (1999), 683-688. Zbl0946.49033MR1724082
  10. [10] R. L. Jerrard – H. M. Soner, Functions of bounded higher variation, Indiana Univ. Math. J., 51 (2002), 645-677. Zbl1057.49036MR1911049
  11. [11] L. Simon, “Lectures on geometric measure theory”, Australian National University, 1984. Zbl0546.49019MR756417
  12. [12] M. Sychev, A new approach to Young measure theory, relaxation and convergence in energy, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 16 (1999), 773-812. Zbl0943.49012MR1720517
  13. [13] B. White, Rectifiability of flat chains, Ann. of Math. (2), 150 (1999), 165-184. Zbl0965.49024MR1715323

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