The Maximum Principle for Minimal Varieties of Arbitrary Codimension

Details The Maximum Principle for Minimal Varieties of Arbitrary Codimension The Maximum Principle for Minimal Varieties of Arbitrary Codimension

2009-05-31

arxiv.org/abs/0906.0189v3

Mathematics

Differential Geometry

8 pages. The new version (posted June 6, 2010) has a few extra explanatory remarks, and an updated bibliographical reference.

Scientific paper

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.

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