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Hölder regularity of two-dimensional almost-minimal sets in ℝ n
Guy David1
1 Mathématiques, Bâtiment 425, Université de Paris-Sud 11, 91 405 Orsay Cedex, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 1, pp. 65-246.

We give a different and probably more elementary proof of a good part of Jean Taylor’s regularity theorem for Almgren almost-minimal sets of dimension 2 in ℝ 3 . We use this opportunity to settle some details about almost-minimal sets, extend a part of Taylor’s result to almost-minimal sets of dimension 2 in ℝ n , and give the expected characterization of the closed sets E of dimension 2 in ℝ 3 that are minimal, in the sense that H 2 (E∖F)≤H 2 (F∖E) for every closed set F such that there is a bounded set B so that F=E out of B and F separates points of ℝ 3 ∖B that E separates.

On donne une démonstration différente et sans doute plus élémentaire d’une bonne partie du résultat de régularité de Jean Taylor sur les ensembles presque-minimaux d’Almgren. On en profite pour donner des précisions sur les ensembles presque minimaux, généraliser une partie du théorème de Taylor aux ensembles presque minimaux de dimension 2 dans ℝ n , et donner la caractérisation attendue des ensembles fermés E de dimension 2 dans ℝ 3 qui sont minimaux, au sens où H 2 (E∖F)≤H 2 (F∖E) pour tout fermé F tel qu’il existe une partie bornée B telle que F=E hors de B et F sépare les points de ℝ 3 ∖B qui sont séparés par E.

DOI: 10.5802/afst.1205

Guy David 1

1 Mathématiques, Bâtiment 425, Université de Paris-Sud 11, 91 405 Orsay Cedex, France 
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Guy David. Hölder regularity of two-dimensional almost-minimal sets in $\mathbb{R}^n$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 1, pp. 65-246. doi : 10.5802/afst.1205. https://afst.centre-mersenne.org/articles/10.5802/afst.1205/

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