On an extension of the H^{k} mean curvature flow

Details On an extension of the H^{k} mean curvature flow On an extension of the H^{k} mean curvature flow

2009-10-06

arxiv.org/abs/0910.1135v1

Mathematics

Differential Geometry

23 pages

Scientific paper

In this note we generalize an extension theorem in [5] and [9] of the mean curvature flow to the H^{k} mean curvature flow under some extra conditions. The main difficult problem in proving the extension theorem is to find a suitable version of Michael-Simon inequality for the H^{k} mean curvature flow, and to do a suitable Moser iteration process. These two problems are overcame by imposing some extra conditions which may be weakened or removed in our forthcoming paper [7]. On the other hand, we derive some estimates for the generalized mean curvature flow, which have their own interesting.

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