An epsilon-regularity theorem for the mean curvature flow

作者：Han, Xiaoli; Sun, Jun^*

来源：Journal of Geometry and Physics, 2012, 62(12): 2329-2336.

DOI：10.1016/j.geomphys.2012.07.009

• Mean curvature flow
• epsilon(0)-regularity
• Hausdorff measure

In this paper, we will derive a small energy regularity theorem for mean curvature flow of arbitrary dimension and codimension. It says that if the parabolic integral of vertical bar A vertical bar(2) around a point in space-time is small, then the mean curvature flow cannot develop singularity at this point. We prove, as an application, that the two-dimensional Hausdorff measure of the singular set of the mean curvature flow from a surface to a Riemannian manifold must be zero.

• 出版日期2012-12
• 单位清华大学