English

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

R2 v1 2026-06-21T13:08:09.407Z