Note on coarea formulae in the Heisenberg group.

Valentino Magnani

Publicacions Matemàtiques (2004)

  • Volume: 48, Issue: 2, page 409-422
  • ISSN: 0214-1493

Abstract

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We show a first nontrivial example of coarea formula for vector-valued Lipschitz maps defined on the three dimensional Heisenberg group. In this coarea formula, integration on level sets is performed with respect to the 2-dimensional spherical Hausdorff measure, built by the Carnot-Carathéodory distance. The standard jacobian is replaced by the so called horizontal jacobian, corresponding to the jacobian of the Pansu differential of the Lipschitz map. Joining previous results, we achieve all possible coarea formulae for Lipschitz maps defined on the Heisenberg group.

How to cite

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Magnani, Valentino. "Note on coarea formulae in the Heisenberg group.." Publicacions Matemàtiques 48.2 (2004): 409-422. <http://eudml.org/doc/41509>.

@article{Magnani2004,
abstract = {We show a first nontrivial example of coarea formula for vector-valued Lipschitz maps defined on the three dimensional Heisenberg group. In this coarea formula, integration on level sets is performed with respect to the 2-dimensional spherical Hausdorff measure, built by the Carnot-Carathéodory distance. The standard jacobian is replaced by the so called horizontal jacobian, corresponding to the jacobian of the Pansu differential of the Lipschitz map. Joining previous results, we achieve all possible coarea formulae for Lipschitz maps defined on the Heisenberg group.},
author = {Magnani, Valentino},
journal = {Publicacions Matemàtiques},
keywords = {Teoría de la medida; Area; Aplicación lipschitziana; Grupo de Heisenberg; coarea formula; Heisenberg group; Carnot-Carathéodory space},
language = {eng},
number = {2},
pages = {409-422},
title = {Note on coarea formulae in the Heisenberg group.},
url = {http://eudml.org/doc/41509},
volume = {48},
year = {2004},
}

TY - JOUR
AU - Magnani, Valentino
TI - Note on coarea formulae in the Heisenberg group.
JO - Publicacions Matemàtiques
PY - 2004
VL - 48
IS - 2
SP - 409
EP - 422
AB - We show a first nontrivial example of coarea formula for vector-valued Lipschitz maps defined on the three dimensional Heisenberg group. In this coarea formula, integration on level sets is performed with respect to the 2-dimensional spherical Hausdorff measure, built by the Carnot-Carathéodory distance. The standard jacobian is replaced by the so called horizontal jacobian, corresponding to the jacobian of the Pansu differential of the Lipschitz map. Joining previous results, we achieve all possible coarea formulae for Lipschitz maps defined on the Heisenberg group.
LA - eng
KW - Teoría de la medida; Area; Aplicación lipschitziana; Grupo de Heisenberg; coarea formula; Heisenberg group; Carnot-Carathéodory space
UR - http://eudml.org/doc/41509
ER -

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