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Hölder regularity of two-dimensional almost-minimal sets in n
Guy David
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 1, p. 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 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 n , and give the expected characterization of the closed sets E of dimension 2 in 3 that are minimal, in the sense that H 2 (EF)H 2 (FE) 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 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 n , et donner la caractérisation attendue des ensembles fermés E de dimension 2 dans 3 qui sont minimaux, au sens où H 2 (EF)H 2 (FE) 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 3 B qui sont séparés par E.

Received : 2007-05-15
Accepted : 2007-11-12
Published online : 2009-05-05
DOI : https://doi.org/10.5802/afst.1205
@article{AFST_2009_6_18_1_65_0,
     author = {Guy David},
     title = {H\"older regularity of two-dimensional almost-minimal sets in $\mathbb{R}^n$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 18},
     number = {1},
     year = {2009},
     pages = {65-246},
     doi = {10.5802/afst.1205},
     zbl = {1213.49051},
     mrnumber = {2518104},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_2009_6_18_1_65_0}
}
David, Guy. 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/item/AFST_2009_6_18_1_65_0/

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