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| The Willmore functional and the containment problem in R~4 | |
| 引用本文： | Jia-zu ZHOU School of Mathematics and Statistics,Southwest University,Chongqing 400715,China, Department of Mathematics,Polytechnic University,Brooklyn,NY 11201,USA. The Willmore functional and the containment problem in R~4[J]. 中国科学A辑(英文版), 2007, 50(3) |
| 作者姓名： | Jia-zu ZHOU School of Mathematics and Statistics Southwest University Chongqing 400715 China Department of Mathematics Polytechnic University Brooklyn NY 11201 USA |
| 作者单位： | Jia-zu ZHOU School of Mathematics and Statistics，Southwest University，Chongqing 400715，China; Department of Mathematics，Polytechnic University，Brooklyn，NY 11201，USA |
| 基金项目： | This work was partially supported by the National Natural Science Foundation of China(Grant No．10671159)，the Funds for Qualified Scientists and Technicians in Guizhou Province of China and Southwest University． |
| 摘 要： | Let∑be a convex hypersurface in the Euclidean space R4 with mean curvature H. We obtain a geometric lower bound for the Willmore functional∫∑H2dσ. This bound is an invariant involving the area of∑, the volume and Minkowski quermassintegrals of the convex body that∑bounds. We also obtain a sufficient condition for a convex body to contain another in the Euclidean space R4. |
The Willmore functional and the containment problem in R~4 |
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| Jia-zu ZHOU. The Willmore functional and the containment problem in R~4[J]. Science in China(Mathematics), 2007, 50(3) | |
| Authors: | Jia-zu ZHOU |
| Affiliation: | School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;Department of Mathematics, Polytechnic University, Brooklyn, NY 11201, USA |
| Abstract: | Let ∑ be a convex hypersurface in the Euclidean space R4 with mean curvature H. We obtain a geometric lower bound for the Willmore functional f∑ H2dσ. This bound is an invariant involving the area of ∑, the volume and Minkowski quermassintegrals of the convex body that ∑bounds. We also obtain a sufficient condition for a convex body to contain another in the Euclidean space R4. |
| Keywords: | mean curvature scalar curvature kinematic formula Minkowski quermassintegrals convex body convex hypersurface. |
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