The Maximum Principle for Minimal Varieties of Arbitrary Codimension
Differential Geometry
2013-04-02 v3
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.
Keywords
Cite
@article{arxiv.0906.0189,
title = {The Maximum Principle for Minimal Varieties of Arbitrary Codimension},
author = {Brian White},
journal= {arXiv preprint arXiv:0906.0189},
year = {2013}
}
Comments
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