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arxiv: 0906.0189 · v3 · pith:IDUNJG4Gnew · submitted 2009-05-31 · 🧮 math.DG

The Maximum Principle for Minimal Varieties of Arbitrary Codimension

classification 🧮 math.DG
keywords minimalprovevarietiesanalogousarbitraryboundaryboundedcannot
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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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