Long-time existence of mean curvature flow with external force fields

Details Long-time existence of mean curvature flow with external force fields Long-time existence of mean curvature flow with external force fields

2006-11-29

arxiv.org/abs/math/0611906v1

Mathematics

Analysis of PDEs

17pages

Scientific paper

In this paper, we study the evolution of submannifold moving by mean curvature minus a external force field. We prove that the flow has a long-time smooth solution for all time under almost optimal conditions. Those conditions are that the second fundamental form on the initial submanifolds is not too large, the external force field, with its any order derivatives, is bounded, and the field is convex with its eigenvalues satisfying a pinch inequality.

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