Paper · Jul 15, 2025

A locally constrained inverse Hessian quotient flow in de Sitter space

Kuicheng Ma

math.DGWider flowsarXiv:2507.11149v2
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Abstract

In this paper, an Alexandrov-Fenchel inequality is established for closed -convex spacelike hypersurface in de Sitter space by investigating the behavior of the locally constrained inverse curvature flow \beginalign \frac{\partial }{\partial t}x=\bigg(u-\fracλ'E_1E_2\bigg)ν,\nonumber \endalign which provides a partial answer to the conjecture raised by Hu and Li in.

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Submitted
Jul 15, 2025
Last revised
Dec 18, 2025 (v2)
Subjects
math.DG

Comments: I realized that there is a serious mistake in Section 4 (on page 9) . More precisely, the uniform upper bound for is unavailable with my argument

Other curvature flowsInverse mean curvature flowVolume-preserving & constrained flowsGeometric inequalitiesPhysics

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  1. Locally constrained inverse curvature flow and Alexandrov-Fenchel type inequalities in de Sitter space

    Kuicheng MaWider flows

    Topics Geometric inequalities, Inverse mean curvature flow, Volume-preserving & constrained flows · Same author Kuicheng Ma · Shared terms “Sitter space”, “locally constrained”, “Alexandrov Fenchel”

  2. Alexandrov-Fenchel inequalities for capillary hypersurfaces in hyperbolic space

    Xinqun Mei and Liangjun WengWider flows

    Topics Geometric inequalities, Inverse mean curvature flow, Volume-preserving & constrained flows · Shared terms “Alexandrov Fenchel”, “locally constrained”, “Fenchel inequalities”

  3. New quermassintegral and Poincaré type inequalities for non-convex domains

    Yingxiang Hu and Mohammad N. IvakiWider flows

    Topics Geometric inequalities, Inverse mean curvature flow, Volume-preserving & constrained flows · Shared terms “locally constrained”, “Alexandrov Fenchel”

  4. New weighted Alexandrov-Fenchel type inequalities and Minkowski inequalities in space forms

    Jie WuWider flows

    Topics Geometric inequalities, Inverse mean curvature flow, Volume-preserving & constrained flows · Shared terms “Alexandrov Fenchel”, “locally constrained”, “Fenchel inequalities”

  5. Michael-Simon type inequalities in hyperbolic space via Brendle-Guan-Li's flows

    Jingshi Cui and Peibiao ZhaoWider flows

    Topics Geometric inequalities, Inverse mean curvature flow, Volume-preserving & constrained flows · Shared terms “locally constrained”, “Alexandrov Fenchel”, “Fenchel inequalities”

  6. A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space

    Yingxiang Hu, Yong Wei, Bo Yang et al.Wider flows

    Topics Geometric inequalities, Inverse mean curvature flow, Volume-preserving & constrained flows · Shared terms “Alexandrov Fenchel”, “Fenchel inequalities”, “locally constrained”

  7. Soliton Solutions to the Curvature Flow on the 2-dimensional De Sitter Space and Applications

    Fábio Nunes da Silva and Edwin Salinas ReyesWider flows

    Topics Inverse mean curvature flow, Physics, Other curvature flows · Shared terms “Sitter space”, “spacelike”

  8. Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary

    Guofang Wang, Liangjun Weng and Chao XiaWider flows

    Topics Geometric inequalities, Volume-preserving & constrained flows, Other curvature flows · Shared terms “Alexandrov Fenchel”, “Fenchel inequalities”, “locally constrained”

Read around it

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) Inverse mean curvature flow Wider flows A hypersurface expands with normal speed 1/H, the reciprocal of its mean curvature. Huisken and Ilmanen's weak version keeps the Hawking mass… Start with: Flow of nonconvex hypersurfaces into spheres (Gerhardt, 1990) Volume-preserving & constrained flows Wider flows Curvature flows with a constraint: subtract the average of the mean curvature and the enclosed volume stays fixed while area decreases, so spheres… Start with: On an area-preserving evolution equation for plane curves (Gage, 1986) 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)