[Une inégalité inverse de type co-aire dans les groupes de Carnot]
Nous démontrons une inégalité de type co-aire pour une fonction entre deux groupes de Carnot munis de distances homogènes. On suppose que la fonction est continûment différentiable au sens de Pansu avec différentielle continue. On suppose aussi que les ensembles de niveau de la fonction sont uniformément inférieurement Ahlfors-réguliers, et que la différentielle de Pansu est partout surjective.
We prove a coarea-type inequality for a continuously Pansu differentiable function acting between two Carnot groups endowed with homogeneous distances. We assume that the level sets of the function are uniformly lower Ahlfors regular and that the Pansu differential is everywhere surjective.
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Keywords: Carnot groups, coarea formula, spherical measure, packing measure.
Mot clés : Groupe de Carnot, formule de co-aire, mesure spherique, mesure de packing.
CC-BY-ND 4.0
@article{AIF_2022__72_1_155_0,
author = {Corni, Francesca},
title = {A reverse coarea-type inequality in {Carnot} groups},
journal = {Annales de l'Institut Fourier},
pages = {155--185},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {72},
number = {1},
year = {2022},
doi = {10.5802/aif.3474},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3474/}
}
TY - JOUR AU - Corni, Francesca TI - A reverse coarea-type inequality in Carnot groups JO - Annales de l'Institut Fourier PY - 2022 SP - 155 EP - 185 VL - 72 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3474/ DO - 10.5802/aif.3474 LA - en ID - AIF_2022__72_1_155_0 ER -
%0 Journal Article %A Corni, Francesca %T A reverse coarea-type inequality in Carnot groups %J Annales de l'Institut Fourier %D 2022 %P 155-185 %V 72 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3474/ %R 10.5802/aif.3474 %G en %F AIF_2022__72_1_155_0
Corni, Francesca. A reverse coarea-type inequality in Carnot groups. Annales de l'Institut Fourier, Tome 72 (2022) no. 1, pp. 155-185. doi : 10.5802/aif.3474. https://aif.centre-mersenne.org/articles/10.5802/aif.3474/
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