Volume preserving flow by powers of k-th mean curvature


题目:Volume preserving flow by powers of k-th mean curvature


时间:2017622日 下午16:00-17:00


摘要:We consider the flow of closed convex hypersurfaces in Euclidean space with the speed given by any positive power of the k-th mean curvature plus a global term such that the volume of the domain enclosed by the flow hypersurface remains constant. We prove that if the initial hypersurface is strictly convex, then the solution of the flow exists for all time and converges to a round sphere smoothly. No curvature pinching assumption is required on the initial hypersurface. The key ingredients include the monotonicity of the mixed volume V_{n+1-k}  along the flow and the Schneider's generalized Alexandrov Theorem for convex bodies with constant curvature measures. In the end of this talk, I will discuss some generalizations and the analogous result in hyperbolic space. This is a joint work with Ben Andrews.