Wulff inequality for minimal submanifolds in Euclidean space

Abstract

In this paper, we prove a Wulff inequality for $n$-dimensional minimal submanifolds with boundary in ${\mathbb{R}}^{n+m}$, where we associate a nonnegative anisotropic weight $\Phi :S^{n+m-1}\to {\mathbb{R}}^{+}$ to the boundary of minimal submanifolds. The Wulff inequality constant depends only on $m$ and $n$, and is independent of the weights. The inequality is sharp if $m=1,2$ and $\Phi$ is the support function of ellipsoids or certain type of centrally symmetric long convex bodies.

arXiv comment17 pages and 1 figure