https://neckpinch.com/authors/jinrong-hu/New arXiv papers by Jinrong Hu, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2311.18606arxiv:2311.18606Thu, 30 Nov 2023 00:00:00 GMTJinrong Hu, Ping Zhang — A variant of the Gauss curvature flow for closed and convex hypersurfaces is considered. We reveal that if the initial hypersurface is pinched enough, then this property is preserved. Furthermore, based on some structure assumptions on the speed function of the shrinking flow, we show that the flow converges to a sphere. This may generalize the result of B. Chow to the possible non-homogeneous curvature flows.Other curvature flowsGauss curvature flowCurvature pinchingHomogeneous spaces https://arxiv.org/abs/2305.00453arxiv:2305.00453Sun, 30 Apr 2023 00:00:00 GMTJinrong Hu, Yong Huang, Jian Lu, Sinan Wang — In this paper, the Lₚ chord Minkowski problem is concerned. Based on the results showed in, we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvature flow for p>−n with p≠ 0.Other curvature flowsGauss curvature flow https://arxiv.org/abs/2302.10537arxiv:2302.10537Tue, 21 Feb 2023 00:00:00 GMTJinrong Hu, Qiongfang Mao — In this paper, we introduce a class of new logarithmic curvature flow. The flows are designed to embrace the monotonicity of the related functional, and the convergence of this flow would tackle the solvability of the weighted Christoffel-Minkowski problem, but a full proof scheme is missing, the key factor of forming this phenomenon lies in the establishment of the upper bound of the principal curvature, which essentially depends on finding a clean condition on smooth positive function defined on the unit sphere sn. Except for obtaining this tricky estimate, we get all the other a priori estimates and hope that this note can attract wide attention to this interesting issue.Other curvature flowsGauss curvature flow https://arxiv.org/abs/2206.01963arxiv:2206.01963Sat, 04 Jun 2022 00:00:00 GMTJinrong Hu, Jiaqian Liu, Di Ma, Jing Wang — In this paper, we concern a generalized fully nonlinear curvature flow involving k-th elementary symmetric function for principal curvature radii in Eulidean space rnnn, k is an integer and 1≤ k≤ n-1. For 1≤ k< n-1, based on some initial data and constrains on smooth positive function defined on the unit sphere sn, we obtain the long time existence and convergence of the flow. Especially, the same result shall be derived for k=n-1 without any constraint on the smooth positive function.Other curvature flowsLong-time existence & convergence