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arXiv · 1609.09665

Inverse mean curvature flows in warped product manifolds

Hengyu Zhou
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Abstract

We study inverse mean curvature flows of starshaped, mean convex hypersurfaces in warped product manifolds with a positive warping factor $\varphi(r)$. If $\varphi'(r)>0$ and $\varphi''(r)\geq 0$, we show that these flows exist for all times, remain starshaped and mean convex. Plus the positivity of $\varphi''(r)$ and a curvature condition we obtain a lower positive bound of mean curvature along these flows independent of the initial mean curvature. We also give a sufficient condition to extend the asymptotic behavior of these flows in Euclidean spaces into some more general warped product manifolds.

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Hengyu Zhou. 2016-09-30. Inverse mean curvature flows in warped product manifolds. https://doi.org/10.1007/s12220-017-9887-z

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