https://neckpinch.com/authors/ling-xiao/New arXiv papers by Ling Xiao, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT 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