https://neckpinch.com/authors/tailong-zhou/New arXiv papers by Tailong Zhou, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2406.05159arxiv:2406.05159Thu, 06 Jun 2024 00:00:00 GMTYong Wei, Bo Yang, Tailong Zhou — We consider the volume preserving flow of smooth, closed and convex hypersurfaces in the hyperbolic space ℍⁿ⁺¹ with speed given by a general nonhomogeneous function of the Gauss curvature. For a large class of speed functions, we prove that the solution of the flow remains convex, exists for all positive time t∈ [0,∞) and converges to a geodesic sphere exponentially as t→∞ in the smooth topology. A key step is to show the L¹ oscillation decay of the Gauss curvature to its average along a subsequence of times going to the infinity, which combined with an argument using the hyperbolic curvature measure theory implies the Hausdorff convergence.Other curvature flowsGauss curvature flowVolume-preserving & constrained flowsHomogeneous spacesLong-time existence & convergence https://arxiv.org/abs/2210.06035arxiv:2210.06035Wed, 12 Oct 2022 00:00:00 GMTYong Wei, Bo Yang, Tailong Zhou — We consider the volume preserving flow of smooth, closed and convex hypersurfaces in the hyperbolic space ℍⁿ⁺¹ (n≥ 2) with the speed given by arbitrary positive power α of the Gauss curvature. We prove that if the initial hypersurface is convex, then the smooth solution of the flow remains convex and exists for all positive time t∈ [0,∞). Moreover, we apply a result of Kohlmann which characterises the geodesic ball using the hyperbolic curvature measures and an argument of Alexandrov reflection to prove that the flow converges to a geodesic sphere exponentially in the smooth topology. This can be viewed as the first result for non-local type volume preserving curvature flows for hypersurfaces in the hyperbolic space with only convexity required on the initial data.Other curvature flowsGauss curvature flowVolume-preserving & constrained flowsLong-time existence & convergence https://arxiv.org/abs/2209.12479arxiv:2209.12479Mon, 26 Sep 2022 00:00:00 GMTYingxiang Hu, Yong Wei, Bo Yang, Tailong Zhou — In this paper, we study the locally constrained inverse curvature flow for hypersurfaces in the half-space with θ-capillary boundary, which was recently introduced by Wang-Weng-Xia. Assume that the initial hypersurface is strictly convex with the contact angle θ∈ (0,π/2]. We prove that the solution of the flow remains to be strictly convex for t>0, exists for all positive time and converges smoothly to a spherical cap. As an application, we prove a complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space with the contact angle θ∈(0,π/2]. Along the proof, we develop a new tensor maximum principle for parabolic equations on compact manifold with proper Neumann boundary condition.Other curvature flowsInverse mean curvature flowVolume-preserving & constrained flowsBoundaries & non-compactFree boundary & capillaryLong-time existence & convergenceGeometric inequalities