题目：Contracting Hypersurfaces by Powers of the \sigma_K-Curvature

报告人🦻🏽：王险峰 副教授（南开大学）

地点：腾讯会议室

时间👨🏻‍💼：2020年12月8日 8:00-9:00

摘要: We investigate the contracting curvature flow of closed, strictly convex axially symmetric hypersurfaces in R^n+1 and S^n+1 by sigma_k^\alpha, where \sigma_k is the k-th elementary symmetric function of the principal curvatures and \alpha\ge 1/k. We prove that for any n\geq3 and any fixed k with 1\leq k\leq n, there exists a constant c(n,k)>0 such that if \alpha lies in the interval [1/k,1/k+c(n,k)], then we have a nice curvature pinching estimate involving the ratio of the biggest principal curvature to the smallest principal curvature at every point of the flow hypersurface, and we prove that the properly rescaled hypersurfaces converge exponentially to the unit sphere. Our results provide an evidence for the general convergence result without initial curvature pinching conditions. This is joint work with Prof. Haizhong Li and Jing Wu.

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