The Maximum Principle for Minimal Varieties of Arbitrary Codimension

Abstract

We prove that an m-dimensional minimal variety in a Riemannian manifold cannot touch the boundary at a point where the sum of the smallest m principal curvatures is greater than 0. We also prove an analogous result for varieties with bounded mean curvature.

8 pages. The new version (posted June 6, 2010) has a few extra explanatory remarks, and an updated bibliographical reference. Newest version (November 11, 2010) has a few typos corrected, including in the statements of theorems 4 and 7