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arXiv · 0906.2981

Mean curvature flow of graphs in warped products

Alexander A. Borisenko·Vicente Miquel
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Abstract

Let $M$ be a complete Riemannian manifold which either is compact or has a pole, and let $φ$ be a positive smooth function on $M$. In the warped product $M\times_φ\mathbb R$, we study the flow by the mean curvature of a locally Lipschitz continuous graph on $M$ and prove that the flow exists for all time and that the evolving hypersurface is $C^\infty$ for $t>0$ and is a graph for all $t$. Moreover, under certain conditions, the flow has a well defined limit.

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Alexander A. Borisenko, Vicente Miquel. 2009-06-16. Mean curvature flow of graphs in warped products. https://arxiv.org/abs/0906.2981

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