A locally constrained inverse Hessian quotient flow in de Sitter space

2025/07/15 by Kuicheng Ma, Ma, Kuicheng
Mathematics · Physics and Astronomy · #53E10 #58J35 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2507.11149

openalex publication_date 2025/07/15 · openalex created_date 2025/10/08 · openalex updated_date 2026/07/28

Abstract

In this paper, an Alexandrov-Fenchel inequality is established for closed 2-convex spacelike hypersurface in de Sitter space by investigating the behavior of the locally constrained inverse curvature flow (∂ )/(∂ t)x=(u-(λ'E₁)/(E₂))ν,which provides a partial answer to the conjecture raised by Hu and Li in \citeHL.

Citations

• Blaschke-Santaló type inequalities and quermassintegral inequalities in space forms
• Geometric inequalities for hypersurfaces with nonnegative sectional curvature in hyperbolic space
• A volume preserving flow and the isoperimetric problem in warped product spaces
• A mean curvature type flow in space forms

Related

• Locally constrained inverse curvature flow and Alexandrov-Fenchel type inequalities in de Sitter space
• Geometric inequalities for convex spacelike hypersurface in de Sitter space
• Alexandrov-Fenchel inequalities for capillary hypersurfaces in hyperbolic space
• A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space
• An Alexandrov-Fenchel-type inequality for hypersurfaces in the sphere