, Volume 126, Issue 3, pp 333-351
Date: 21 Mar 2008

Forced convex mean curvature flow in Euclidean spaces

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Abstract

We show the mean curvature flow of convex hypersurfaces in Euclidean spaces with a general forcing term 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 converge to a round sphere in special cases. Long time existence and convergence of the normalization of the flow are studied.

The first author is partially supported by NSFC (No.10501011) and by Fundação Ciência e Tecnologia (FCT) through a FCT fellowship SFRH/BPD/26554/2006. The second author is partially supported by FCT through the Plurianual of CFIF and POCI/MAT/60671/2004.