2 9 N ov 2 00 6 Long - time existence of mean curvature flow with external force fields ∗
نویسنده
چکیده
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 longtime 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.
منابع مشابه
Brian White - Mean Curvature Flow (math 258) Lecture Notes Notes by Otis Chodosh
1. Overview 2 1.1. Curve shortening flow 2 1.2. Flow of hypersurfaces 5 1.3. Mean convex surfaces 6 2. The maximum principle 7 3. Unparameterized mean curvature flow 8 3.1. Graphs 8 4. Short-time existence and smoothing 9 5. Long term behavior of mean curvature flow 9 6. Renormalized mean curvature flow 11 7. The level set approach to weak limits 13 8. Weak compactness of submanifolds 16 8.1. E...
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