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arXiv · 1712.06838

Mean Curvature Type Flows of Graphs in Product Manifolds

Aijin Lin·Hengyu Zhou
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Abstract

In this note we study a large class of mean curvature type flows of graphs in product manifold $N\times R$ where N is a closed Riemann- ian manifold. Their speeds are the mean curvature of graphs plus a prescribed function. We establish long time existence and uniformly convergence of those flows with a barrier condition and a condition on the derivative of prescribed function with respect to the height. As an application we construct a weighted mean curvature flow in large classes of warped product manifolds which evolves each graph into a totally ge- odesic slice

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Aijin Lin, Hengyu Zhou. 2017-12-19. Mean Curvature Type Flows of Graphs in Product Manifolds. https://arxiv.org/abs/1712.06838

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