## Hölder regularity of two-dimensional almost-minimal sets in $$\mathbb R^n$$.(English)Zbl 1213.49051

Summary: 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 $$H^2(E\setminus F)\leq H^2 (F\setminus E)$$ 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 $$\mathbb R^3\setminus B$$ that $$E$$ separates.

### MSC:

 49Q20 Variational problems in a geometric measure-theoretic setting 49N60 Regularity of solutions in optimal control
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### References:

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