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arXiv · 1708.06049

Mean Curvature Flows of Closed Hypersurfaces in Warped Product Manifolds

Zheng Huang·Zhou Zhang·Hengyu Zhou
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Abstract

We investigate the mean curvature flows in a class of warped product manifolds with closed hypersurfaces fibering over $\mathbb{R}$. In particular, we prove that under natural conditions on the warping function and Ricci curvature bound for the ambient space, there exists a large class of closed initial hypersurfaces, as geodesic graphs over the totally geodesic hypersurface $\Sigma$, such that the mean curvature flow starting from $S_0$ exists for all time and converges to $\Sigma$.

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Zheng Huang, Zhou Zhang, Hengyu Zhou. 2017-08-21. Mean Curvature Flows of Closed Hypersurfaces in Warped Product Manifolds. https://arxiv.org/abs/1708.06049

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