A geometric inequality on hypersurface in hyperbolic space

2012/11/17 by Haizhong Li, Yong Wei, Changwei Xiong · 2 citations
Mathematics · #Curvature #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Hyperbolic space #Hypersurface #Inequality #Inverse #Mathematical analysis #Mathematics #Mean curvature #Mean curvature flow #Point processes and geometric inequalities #Pure mathematics #Regular polygon #Space (punctuation) #math.DG

paper · pdf · doi:10.1016/j.aim.2013.12.003

published as Advances in Mathematics., 2014, 253(1):152-162 · 9 pages. All comments are welcome

arxiv created 2012/11/17 · openalex publication_date 2013/12/25 · arxiv updated 2017/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, we use the inverse curvature flow to prove a sharp geometric inequality on star-shaped and two-convex hypersurface in hyperbolic space.

Citations

• Flow by mean curvature of convex surfaces into spheres
• Convexity estimates for mean curvature flow and singularities of mean convex surfaces
• A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold
• Quasilocal mass and surface Hamiltonian in spacetime

Cited by

• The Gauss–Bonnet–Chern mass for graphic manifolds
• The Minkowski inequality in de Sitter space