https://neckpinch.com/authors/fang-hong/New arXiv papers by Fang Hong, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2603.19646/arxiv:2603.19646Fri, 20 Mar 2026 00:00:00 GMTFang Hong — In this paper, we prove a sharp Minkowski-type inequality in Cartan-Hadamard 3-spaces using harmonic mean curvature flow and improve the known estimates for total mean curvature in hyperbolic 3-space. In particular, we sharpen Ghomi-Spruck's result in by retaining the volume contribution in the monotonicity argument. As a corollary, we obtain a comparison theorem relating the total mean curvature of convex surfaces in Cartan-Hadamard 3-spaces to their enclosed volume.Mean curvature flowGeometric inequalities https://neckpinch.com/papers/2111.10170/arxiv:2111.10170Fri, 19 Nov 2021 00:00:00 GMTFang Hong — In this paper, we study a class of flows of closed, star-shaped hypersurfaces in hyperbolic space ℍⁿ⁺¹ with speed (sinh r)^(α/β) σₖ^(1/β), where σₖ is the k-th elementary symmetric polynomial of the principal curvatures, α, β are positive constants and r is the distance from points on the hypersurface to the origin. We obtain convergence results under some assumptions of k, α and β. When k = 1 , α> 1 + β, and the initial hypersurface is mean convex, we prove that the mean convex solution to the flow for k=1 exists for all time and converges smoothly to a sphere. When 1≤ k ≤ n, α> k+β, and the initial hypersurface is uniformly convex, we prove that the uniformly convex solution to the flow exists for all time and converges smoothly to a sphere. In particular, we generalize Li-Sheng-Wang's results from Euclidean space to hyperbolic space.Other curvature flowsLong-time existence & convergence