Published Paper

Inserted: 11 sep 1998
Last Updated: 16 mar 2022

Journal: manuscripta math.
Volume: 97
Pages: 15-35
Year: 1998
Doi: 10.1007/s002290050082

Abstract:

Let $E_0\subset R^n$ be a minimal set with mean curvature in $L^n$ that is a minimum of the functional $E\mapsto P(E,\Omega)+\int_{E\cap\Omega} H$, where $\Omega\subset R^n$ is open and $H\in L^n(\Omega)$. We prove that if $2\le n\le 7$ then $\partial E_0$ can be parametrized over the $(n-1)$-dimensional disk with a $C^{0,\alpha}$ mapping with $C^{0,\alpha}$ inverse.

Keywords: regularity, minimal surfaces

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