https://neckpinch.com/authors/zhou-zhang/New arXiv papers by Zhou Zhang, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2311.04298arxiv:2311.04298Tue, 07 Nov 2023 00:00:00 GMTZheng Huang, Longzhi Lin, Zhou Zhang — There has been a conjecture, often attributed to Thurston, which asserts that every almost Fuchsian manifold is foliated by closed incompressible constant mean curvature (CMC) surfaces. In this paper, for a certain class of almost Fuchsian manifolds, we prove the long-time existence and convergence of the modified mean curvature flow ∂F/∂t=−(H-c)vecν, which was first introduced by Xiao and the second named author in. As an application, we confirm Thurston's CMC foliation conjecture for such a subclass of almost Fuchsian manifolds.Mean curvature flowGeometrizationLong-time existence & convergence https://arxiv.org/abs/2308.12527arxiv:2308.12527Thu, 24 Aug 2023 00:00:00 GMTHosea Wondo, Zhou Zhang — In this paper, we show that the singularity type of solutions to the Käher-Ricci flow on a numerically effective manifold does not depend on the initial metric. More precisely if there exists a type III solution to the Kähler-Ricci flow, then any other solution starting from a different initial metric will also be Type III. This generalises previous results by Y. Zhang for the semi-ample case.Ricci flowKähler–Ricci flowSingularitiesKähler geometryLong-time existence & convergenceAnalytic minimal model programNumerics & visualization https://arxiv.org/abs/2210.10296arxiv:2210.10296Wed, 19 Oct 2022 00:00:00 GMTHaotian Wu, Zhou Zhang — We improve the understanding of both finite time and infinite time singularities of the modified Kähler-Ricci flow as initiated by the second author of this paper in [26]. This is done by relating the modified Kähler-Ricci flow with the recent studies on the classic Kähler-Ricci flow and the degenerate complex Monge-Ampère equation.Ricci flowKähler–Ricci flowSingularitiesKähler geometry https://arxiv.org/abs/2107.13127arxiv:2107.13127Wed, 28 Jul 2021 00:00:00 GMTZheng Huang, Longzhi Lin, Zhou Zhang — We consider the dynamic property of the volume preserving mean curvature flow. This flow was introduced by Huisken who also proved it converges to a round sphere of the same enclosed volume if the initial hypersurface is strictly convex in Euclidean space. We study the stability of this flow in hyperbolic space. In particular, we prove that if the initial hypersurface is hyperbolically mean convex and close to an umbilical sphere in the L²-sense, then the flow exists for all time and converges exponentially to an umbilical sphere.Mean curvature flowVolume-preserving & constrained flowsStability & uniquenessLong-time existence & convergence