Ancient solution of mean curvature flow of arbitrary codimension

Abstract: In this talk, we will discuss rigidity problem of ancient solutions of the mean curvature flow with arbitrary codimension in space forms. We first prove that under certain sharp pointwise curvature pinching condition the ancient solution in a sphere is either a shrinking spherical cap or a totally geodesic sphere. Then we show that under certain pointwise curvature pinching condition the ancient solution in a hyperbolic space is a family of shrinking spheres. We also obtain a rigidity result for ancient solutions in a nonnegatively curved space form under an integral curvature pinching condition. This is joint work with Prof. H. W. Xu and Prof. E. T. Zhao.

Mathematics

Audience: researchers in the topic

ICCM 2020