The Mean Curvature Flow Smoothes Lipschitz Submanifolds

Details The Mean Curvature Flow Smoothes Lipschitz Submanifolds The Mean Curvature Flow Smoothes Lipschitz Submanifolds

2002-09-14

arxiv.org/abs/math/0209176v2

Mathematics

Differential Geometry

revised version. Part of the proof of Theorem A has been rewritten

Scientific paper

The mean curvature flow is the gradient flow of volume functionals on the space of submanifolds. We prove a fundamental regularity result of the mean curvature flow in this paper: a Lipschitz submanifold with small local Lipschitz norm becomes smooth instantly along the mean curvature flow. This generalizes the regularity theorem of Ecker and Huisken for Lipschitz hypersurfaces. In particular, any submanifold of the Euclidean space with a continuous induced metric can be smoothed out by the mean curvature flow. The smallness assumption is necessary in the higher codimension case in view of an example of Lawson and Osserman. The stationary phase of the mean curvature flow corresponds to minimal submanifolds. Our result thus generalizes Morrey's classical theorem on the smoothness of $C^1$ minimal submanifolds.

Affiliated with

Also associated with

No associations

Rating

The Mean Curvature Flow Smoothes Lipschitz Submanifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Mean Curvature Flow Smoothes Lipschitz Submanifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Mean Curvature Flow Smoothes Lipschitz Submanifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-356492