题目：Volume preserving flow by powers of k-thmeancurvature

报告人：韦勇（澳大利亚国立大学博士后）

时间：2017年6月22日 下午16:00-17:00

地点：理科楼B203

摘要：We consider the flow of closed convexhypersurfacesin Euclidean space with the speed given by any positive power of the k-thmean curvature plus a global term such that the volume of the domain enclosed by the flowhypersurfaceremains constant. We prove that if the initialhypersurfaceis 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 initialhypersurface. The key ingredients include the monotonicity of the mixed volume V_{n+1-k} along the flow and the Schneider's generalizedAlexandrovTheorem 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.

联系人：陈大广