The Willmore functional and the containment problem in R4 |
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| Authors: | Jia-zu Zhou |
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| Affiliation: | 1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China
2. Department of Mathematics, Polytechnic University, Brooklyn, NY, 11201, USA
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| Abstract: | Let Σ be a convex hypersurface in the Euclidean space R 4 with mean curvature H. We obtain a geometric lower bound for the Willmore functional ∫Σ H 2 dσ. This bound is an invariant involving the area of Σ, the volume and Minkowski quermassintegrals of the convex body that Σ bounds. We also obtain a sufficient condition for a convex body to contain another in the Euclidean space R 4. |
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