Hölder Regularity of Two-Dimensional Almost-Minimal Sets in $\R^n$

Details Hölder Regularity of Two-Dimensional Almost-Minimal Sets in $\R^n$ Hölder Regularity of Two-Dimensional Almost-Minimal Sets in $\R^n$

2008-06-10

arxiv.org/abs/0806.1645v1

Mathematics

Classical Analysis and ODEs

150 pages. Submitted in May 2007

Scientific paper

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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