Geometric inequalities for convex spacelike hypersurface in de Sitter space

2025/09/26 by Dong, Yandi, Ma, Kuicheng
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.22470

Abstract

In this paper, the long-time existence and convergence results are derived for locally constrained flows with initial value some compact spacelike hypersurface that is suitably pinched in the de Sitter space. As applications, geometric inequalities related to the quermassintegrals as well as the weighted curvature integrals are established.

Citations

• Blaschke-Santaló type inequalities and quermassintegral inequalities in space forms
• Geometric inequalities for static convex domains in hyperbolic space
• A volume preserving flow and the isoperimetric problem in warped product spaces
• Pinching estimates and motion of hypersurfaces by curvature functions

Related

• Locally constrained inverse curvature flow and Alexandrov-Fenchel type inequalities in de Sitter space
• A locally constrained inverse Hessian quotient flow in de Sitter space
• Geometric inequalities for static convex domains in hyperbolic space
• Locally constrained flows and geometric inequalities in sphere
• Alexandrov-Fenchel inequalities for capillary hypersurfaces in hyperbolic space