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]
Liang, Xiangyu1
1 Institut Camille Jordan Université Claude Bernard Lyon 1 43 boulevard du 11 novembre 1918 69622 Villeurbanne cedex (France)
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 :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3058
Classification : 28A75, 49Q10, 49Q20, 49K99
Keywords: Minimal sets, blow-in limit, existence of singularities, Hausdorff measure, elliptic systems
Mot clés : Ensembles minimaux, limites d’explosion, existence de singularités, mesure de Hausdorff, système elliptiques.
Liang, Xiangyu 1

1 Institut Camille Jordan Université Claude Bernard Lyon 1 43 boulevard du 11 novembre 1918 69622 Villeurbanne cedex (France) 
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.3058/

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