HÖLDER REGULARITY OF TWO-DIMENSIONAL ALMOST-MINIMAL SETS IN $\R^n$
Résumé
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 $H^2(E\setminus F) \leq H^2(F\setminus E)$ 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 $\R^3 \setminus B$ that $E$ separates.
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JT+-pour-Hal.pdf (1.04 Mo)
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JT_-pour-Hal.pdf (1.15 Mo)
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Origine : Fichiers produits par l'(les) auteur(s)
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