no. 5
Global regularity for minimal sets near a union of two planes  [ Régularité globale pour les ensembles minimaux proche d’une union de deux plans ]
Annales de l'Institut Fourier, Tome 66 (2016) no. 5, pp. 2067-2099.

On traite la régularité globale des ensembles minimaux 2-dimensionnels qui sont proches d’une union de deux plans, et on démontre que tout ensemble minimal proche d’une union de deux plans presque orthogonaux à l’infini dans ℝ 4 est un cône. L’enjeu est de contrôler le comportement d’un ensemble minimal à petite échelle par la topologie à grande échelle.

We discuss the global regularity of 2 dimensional minimal sets that are near a union of two planes, and prove that every global minimal set in ℝ 4 that looks like a union of two almost orthogonal planes at infinity is a cone. The main point is to use the topological properties of a minimal set at a large scale to control its behavior at smaller scales.

Reçu le : 2012-05-04
Révisé le : 2013-01-20
Accepté le : 2013-09-01
Publié le : 2016-07-27
DOI : https://doi.org/10.5802/aif.3058
Classification : 28A75,  49Q10,  49Q20,  49K99
Mots clés : Ensembles minimaux, limites d’explosion, existence de singularités, mesure de Hausdorff, système elliptiques. 
@article{AIF_2016__66_5_2067_0,
     author = {Liang, Xiangyu},
     title = {Global regularity for minimal sets near a union of two planes},
     journal = {Annales de l'Institut Fourier},
     pages = {2067--2099},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {5},
     year = {2016},
     doi = {10.5802/aif.3058},
     language = {en},
     url = {www.numdam.org/item/AIF_2016__66_5_2067_0/}
}
Liang, Xiangyu. Global regularity for minimal sets near a union of two planes. Annales de l'Institut Fourier, Tome 66 (2016) no. 5, pp. 2067-2099. doi : 10.5802/aif.3058. http://www.numdam.org/item/AIF_2016__66_5_2067_0/

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