Regularity of sets with constant intrinsic normal in a class of Carnot groups  [ Régularité des ensembles à normale intrinsèque constante dans une classe de groupes de Carnot ]
Annales de l'Institut Fourier, Tome 64 (2014) no. 2, pp. 429-455.

Dans cette note, nous définissons une classe de groupes de Lie stratifiés de pas arbitraire (que nous appelons “groupes de type ” dans cet article), et nous montrons que, dans ces groupes, les ensembles à normale intrinsèque constante sont des hyperplans. En conséquence, la frontière réduite d’un ensemble de périmètre intrinsèque fini dans un groupe de type est rectifiable au sens intrinsèque (théorème de rectifiabilité de De Giorgi). Ce résultat étend un résultat précédent prouvé par Franchi, Serapioni & Serra Cassano pour les groupes de pas 2.

In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano in step 2 groups.

DOI : https://doi.org/10.5802/aif.2853
Classification : 28A75,  49Q15,  58C35
Mots clés : Groupes de Carnot, périmètre intrinsèque, rectifiabilité intrinsèque
@article{AIF_2014__64_2_429_0,
     author = {Marchi, Marco},
     title = {Regularity of sets with constant intrinsic normal in a class of Carnot groups},
     journal = {Annales de l'Institut Fourier},
     pages = {429--455},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {2},
     year = {2014},
     doi = {10.5802/aif.2853},
     mrnumber = {3330910},
     zbl = {06387280},
     language = {en},
     url = {archive.numdam.org/item/AIF_2014__64_2_429_0/}
}
Marchi, Marco. Regularity of sets with constant intrinsic normal in a class of Carnot groups. Annales de l'Institut Fourier, Tome 64 (2014) no. 2, pp. 429-455. doi : 10.5802/aif.2853. http://archive.numdam.org/item/AIF_2014__64_2_429_0/

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