https://neckpinch.com/authors/jing-wu/New arXiv papers by Jing Wu, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1905.05571/arxiv:1905.05571Tue, 14 May 2019 00:00:00 GMTHaizhong Li, Xianfeng Wang, Jing Wu — In this paper, we investigate the contracting curvature flow of closed, strictly convex axially symmetric hypersurfaces in ℝⁿ⁺¹ and Sⁿ⁺¹ by σₖ^α, where σₖ is the k-th elementary symmetric function of the principal curvatures and α≥ 1/k. We prove that for any n≥3 and any fixed k with 1≤ k≤ n, there exists a constant c(n,k)>1/k such that that if α lies in the interval [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 of the flow hypersurface, and we prove that the properly rescaled hypersurfaces converge exponentially to the unit sphere. In the case 1<k≤ n ≤ k², we can choose c(n,k)=1/(k-1). Our results provide an evidence for the general convergence result without initial curvature pinching conditions.Other curvature flowsCurvature pinchingLong-time existence & convergenceRotational symmetry & warped products