https://neckpinch.com/authors/dake-li/New arXiv papers by Dake Li, from Neckpinch Tue, 03 Nov 2026 07:43:57 GMT https://neckpinch.com/papers/2608.20037/arxiv: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://neckpinch.com/papers/2606.14082/arxiv: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