Note on coarea formulae in the Heisenberg group.

Valentino Magnani

Publicacions Matemàtiques (2004)

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

Abstract

top
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

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.