| Complete bounded λ-hypersurfaces in the weighted volume-preserving mean curvature flow |
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| 摘 要： | In this paper, we study the complete bounded λ-hypersurfaces in the weighted volume-preserving mean curvature flow. Firstly, we investigate the volume comparison theorem of complete bounded λ-hypersurfaces with |A|≤α and get some applications of the volume comparison theorem. Secondly, we consider the relation among λ, extrinsic radius k, intrinsic diameter d, and dimension n of the complete λ-hypersurface,and we obtain some estimates for the intrinsic diameter and the extrinsic radius. At last, we get some topological properties of the bounded λ-hypersurface with some natural and general restrictions.
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Complete bounded λ-hypersurfaces in the weighted volume-preserving mean curvature flow |
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| Authors: | Yecheng Zhu Yi Fang Qing Chen |
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| Institution: | 1.Department of Mathematics,University of Science and Technology of China,Hefei,China;2.Department of Applied Mathematics,Anhui University of Technology,Maanshan,China |
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| Abstract: | In this paper, we study the complete bounded λ-hypersurfaces in the weighted volume-preserving mean curvature flow. Firstly, we investigate the volume comparison theorem of complete bounded λ-hypersurfaces with |A| ? α and get some applications of the volume comparison theorem. Secondly, we consider the relation among λ, extrinsic radius k, intrinsic diameter d, and dimension n of the complete λ hypersurface, and we obtain some estimates for the intrinsic diameter and the extrinsic radius. At last, we get some topological properties of the bounded λ-hypersurface with some natural and general restrictions. |
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