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

2025/12/22 by Kuicheng Ma, Ma, Kuicheng
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.2512.19285

openalex publication_date 2025/12/22 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the behavior of some locally constrained inverse curvature flow in de Sitter space, with initial value any closed spacelike k-convex hypersurface satisfying some pinching condition. Assume further the Heintze-Karcher inequality for any closed spacelike mean convex hypersurface in de Sitter space, we derive a class of Alexandrov-Fenchel inequalities.

Citations

• Blaschke-Santaló type inequalities and quermassintegral inequalities in space forms
• Geometric inequalities for static convex domains in hyperbolic space
• Minkowski formulae and Alexandrov theorems in spacetime
• Constant mean curvature surfaces in warped product manifolds
• Pinching estimates and motion of hypersurfaces by curvature functions

Related

• A locally constrained inverse Hessian quotient flow in de Sitter space
• Geometric inequalities for convex spacelike hypersurface in de Sitter space
• Alexandrov-Fenchel inequalities for capillary hypersurfaces in hyperbolic space
• New quermassintegral and Poincaré type inequalities for non-convex domains
• A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space