Forced Convex Mean Curvature Flow in Euclidean Spaces

Details Forced Convex Mean Curvature Flow in Euclidean Spaces Forced Convex Mean Curvature Flow in Euclidean Spaces

2007-11-15

arxiv.org/abs/0711.2366v1

Manuscripta Math. 126 (2008) 333 - 351

Mathematics

Differential Geometry

22 Pages

Scientific paper

10.1007/s00229-008-0181-z

In this paper, we consider the mean curvature flow of convex hypersurfaces in Euclidean spaces with a general forcing term. We show that the flow may shrink to a point in finite time if the forcing term is small, or exist for all times and expand to infinity if the forcing term is large enough. The flow can also converge to a round sphere for some special forcing term and initial hypersurface. Furthermore, the normalization of the flow is carried out so that long time existence and convergence of the rescaled flow are studied. Our work extends Huisken's well-known mean curvature flow and McCoy's mixed volume preserving mean curvature flow.

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