https://neckpinch.com/authors/zhizhang-wang/New arXiv papers by Zhizhang Wang, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.20037arxiv:2608.20037Thu, 20 Aug 2026 00:00:00 GMTDake Li, Zhizhang Wang, Shiqi Yin — This paper studies self-shrinkers and the long-time behavior of the inverse σₖ curvature flow for noncompact entire spacelike strictly convex hypersurfaces in Minkowski space. In contrast to the co-compact setting, where the corresponding self-shrinker is rigid, the noncompact problem admits a rich family of self-shrinkers determined by their asymptotic data. More precisely, we formulate the self-shrinker equation as a fully nonlinear Dirichlet problem on hyperbolic space with prescribed data on its ideal boundary, and prove that every continuous negative boundary value determines a unique entire spacelike strictly convex self-shrinker. We further study the inverse σₖ curvature flow starting from an entire spacelike strictly convex hypersurface satisfying a subsolution condition at infinity and a uniform positive lower bound for its σₖ curvature. We prove global existence of the flow and show that the normalized flow converges locally smoothly to the unique self-shrinker with the same prescribed boundary value at infinity.Other curvature flowsSelf-shrinkers & translatorsBoundaries & non-compactLong-time existence & convergencePhysics https://arxiv.org/abs/2606.14082arxiv:2606.14082Fri, 12 Jun 2026 00:00:00 GMTDake Li, Zhizhang Wang, Shiqi Yin — In this paper, we investigate the cocompact inverse σₖ curvature flow in Minkowski space. We prove the longtime existence and convergence of this flow. As a consequence, quermassintegral inequalities are established.Other curvature flowsLong-time existence & convergenceGeometric inequalities https://arxiv.org/abs/2505.23067arxiv:2505.23067Thu, 29 May 2025 00:00:00 GMTRongli Huang, Changzheng Qu, Zhizhang Wang, Weifeng Wo — We investigate the evolution of strictly convex hypersurfaces driven by the k-Hessian curvature flow, subject to the second boundary condition. We first explore the translating solutions corresponding to this boundary value problem. Next, we establish the long-time existence of the flow and prove that it converges to a translating solution. To overcome the difficulty of driving boundary C² estimates, we employ an orthogonal invariance technique. Using this method, we extend the results of Schnürer-Smoczyk and Schnürer from the second boundary value problem of Gauss curvature flow to k-Hessian curvature flow.Other curvature flowsGauss curvature flowSelf-shrinkers & translatorsBoundaries & non-compactLong-time existence & convergence https://arxiv.org/abs/2409.07301arxiv:2409.07301Wed, 11 Sep 2024 00:00:00 GMTQu Changzheng, Wang Zhizhang, Wo Weifeng — In this paper, we study the k-Hessian curvature flow of noncompact spacelike hypersurfaces in Minkowski space. We first prove the existence of translating solutions with given asymptotic behavior. Then, we prove that for strictly convex initial hypersurface satisfying certain conditions, the curvature flow exists for all time, and the normalized flow converges to a translating solution.Other curvature flowsSelf-shrinkers & translatorsBoundaries & non-compactLong-time existence & convergencePhysics https://arxiv.org/abs/2207.04552arxiv:2207.04552Sun, 10 Jul 2022 00:00:00 GMTZhizhang Wang, Ling Xiao — In this paper, we study the σₖ curvature flow of noncompact spacelike hypersurfaces in Minkowski space. We prove that if the initial hypersurface satisfies certain conditions, then the flow exists for all time. Moreover, we show that after rescaling, the flow converges to a self-expander.Other curvature flowsSelf-shrinkers & translatorsBoundaries & non-compactLong-time existence & convergencePhysics https://arxiv.org/abs/2205.06853arxiv:2205.06853Fri, 13 May 2022 00:00:00 GMTZhizhang Wang, Ling Xiao — In [19], we prove that if an entire, spacelike, convex hypersurface 𝓜_(u₀) has bounded principal curvatures, then the σₖ^(1/α) (power of σₖ) curvature flow starting from 𝓜_(u₀) admits a smooth convex solution u for t>0. Moreover, after rescaling, the flow converges to a convex self-expander 𝓜=\(x, u(x))mid x∈ℝⁿ\ that satisfies σₖ(κ[𝓜])=(-<X₀, ν₀>)^α. Unfortunately, the existence of self-expander for power of σₖ curvature flow in Minkowski space has not been studied before. In this paper, we fill the gap.Other curvature flowsSelf-shrinkers & translatorsPhysics https://arxiv.org/abs/2205.06849arxiv:2205.06849Fri, 13 May 2022 00:00:00 GMTZhizhang Wang, Ling Xiao — In this paper, we study fully nonlinear curvature flows of noncompact spacelike hypersurfaces in Minkowski space. We prove that if the initial hypersurface satisfies certain conditions, then the flow exists for all time. Moreover, we show that after rescaling the flow converges to the future timelike hyperboloid, which is a self-expander.Other curvature flowsSelf-shrinkers & translatorsBoundaries & non-compactLong-time existence & convergencePhysics