Paper · Jun 12, 2026

Inverse Hessian Curvature Flow in Minkowski Space I: Cocompact Hypersurfaces

Dake Li, Zhizhang Wang, Shiqi Yin

math.DGWider flowsarXiv:2606.14082v2
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Abstract

In this paper, we investigate the cocompact inverse 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

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Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Entire convex curvature flow in Minkowski space (Zhizhang Wang and Ling Xiao, 2022)5Wang 2022 Entire self-expanders for power of σₖ curvature flow in Minkowski space (Zhizhang Wang and Ling Xiao, 2022)6Wang 2022 Entire σₖ curvature flow in Minkowski space (Zhizhang Wang and Ling Xiao, 2022)2Wang 2022 Stability of quermassintegral inequalities along inverse curvature flows (Caroline VanBlargan and Yi Wang, 2022)8VanBlargan 2022 Translating solutions and the entire Hessian curvature flow in Minkowski space (Qu Changzheng, Wang Zhizhang and Wo Weifeng, 2024)3Changzheng 2024 Second boundary value problem for the Hessian curvature flow (Rongli Huang, Changzheng Qu, Zhizhang Wang et al., 2025)4Huang 2025 A locally constrained inverse Hessian quotient flow in de Sitter space (Kuicheng Ma, 2025)7Ma 2025 Inverse Hessian Curvature Flow in Minkowski Space II: The Dirichlet problem at infinity (Dake Li, Zhizhang Wang and Shiqi Yin, 2026)1Li 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Inverse Hessian Curvature Flow in Minkowski Space II: The Dirichlet problem at infinity

    Dake Li, Zhizhang Wang and Shiqi YinWider flows PDF

    Topics Long-time existence & convergence, Other curvature flows · Same authors Dake Li, Zhizhang Wang, Shiqi Yin · Shared terms “inverse hessian”, “Hessian curvature”, “Minkowski space”

  2. Entire curvature flow in Minkowski space

    Zhizhang Wang and Ling XiaoWider flows PDF

    Topics Long-time existence & convergence, Other curvature flows · Same author Zhizhang Wang · Shared terms “Minkowski space”

  3. Translating solutions and the entire Hessian curvature flow in Minkowski space

    Qu Changzheng, Wang Zhizhang and Wo WeifengWider flows PDF

    Topics Long-time existence & convergence, Other curvature flows · Shared terms “Hessian curvature”, “Minkowski space”

  4. Second boundary value problem for the Hessian curvature flow

    Rongli Huang, Changzheng Qu, Zhizhang Wang et al.Wider flows PDF

    Topics Long-time existence & convergence, Other curvature flows · Same author Zhizhang Wang · Shared terms “Hessian curvature”

  5. Entire convex curvature flow in Minkowski space

    Zhizhang Wang and Ling XiaoWider flows PDF

    Topics Long-time existence & convergence, Other curvature flows · Same author Zhizhang Wang · Shared terms “Minkowski space”

  6. Entire self-expanders for power of curvature flow in Minkowski space

    Zhizhang Wang and Ling XiaoWider flows PDF

    Topics Other curvature flows · Same author Zhizhang Wang · Shared terms “Minkowski space”

  7. A locally constrained inverse Hessian quotient flow in de Sitter space

    Kuicheng MaWider flows PDF

    Topics Geometric inequalities, Other curvature flows · Shared terms “inverse hessian”

  8. Stability of quermassintegral inequalities along inverse curvature flows

    Caroline VanBlargan and Yi WangWider flows PDF

    Topics Geometric inequalities, Other curvature flows · Shared terms “quermassintegral inequalities”

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Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Other curvature flows Wider flows Flows that move a hypersurface or metric by some other function of curvature: Gauss curvature (worn stones), inverse mean curvature (the Penrose… Start with: Shapes of worn stones (Firey, 1974) Long-time existence & convergence A geometric flow either runs forever or stops because something blows up. Extension criteria say which quantity must blow up at a finite singular… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) Geometric inequalities Sharp inequalities between area, volume and integrals of curvature, with equality only for round spheres. Start with: Mean curvature flow and geometric inequalities (Topping, 1998)