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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 Sér. 6, 18 no. 1 (2009), p. 65-246, doi: 10.5802/afst.1205
Article PDF | Reviews MR 2518104 | Zbl 1213.49051 | 3 citations in Cedram

Résumé - Abstract

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 ${\mathbb{R}}^3$. 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 $\mathbb{R}^n$, and give the expected characterization of the closed sets $E$ of dimension $2$ in ${\mathbb{R}}^3$ that are minimal, in the sense that $H^2(E\setminus F) \le H^2(F\setminus E)$ 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 ${\mathbb{R}}^3 \setminus B$ that $E$ separates.

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