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arXiv · 1702.03428

Complete bounded $\lambda$-hypersurfaces in the weighted volume-preserving mean curvature flow

Yecheng Zhu·Yi Fang·Qing Chen
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Abstract

In this paper, we study the complete bounded $\lambda$-hypersurfaces in weighted volume-preserving mean curvature flow. Firstly, we investigate the volume comparison theorem of complete bounded $\lambda$-hypersurfaces with $|A|\leq\alpha$ and get some applications of the volume comparison theorem. Secondly, we consider the relation among $\lambda$, extrinsic radius $k$, intrinsic diameter $d$, and dimension $n$ of the complete $\lambda$-hypersurface, and we obtain some estimates for the intrinsic diameter and the extrinsic radius. At last, we get some topological properties of the bounded $\lambda$-hypersurface with some natural and general restrictions.

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Yecheng Zhu, Yi Fang, Qing Chen. 2017-02-11. Complete bounded $\lambda$-hypersurfaces in the weighted volume-preserving mean curvature flow. https://doi.org/10.1007/s11425-016-9020-9

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