A geometric inequality on hypersurface in hyperbolic space

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.

9 pages. All comments are welcome

References in corpus (2)

• A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold
• Quasilocal mass and surface Hamiltonian in spacetime

Cited by in corpus (29)

• Volume preserving flow and Alexandrov-Fenchel type inequalities in hyperbolic space
• Locally constrained curvature flows and geometric inequalities in hyperbolic space
• Quermassintegral preserving curvature flow in Hyperbolic space
• Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball
• Alexandrov-Fenchel type inequalities for convex hypersurfaces in hyperbolic space and in sphere
• On inverse mean curvature flow in Schwarzschild space and Kottler space
• Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary
• A geometric inequality for convex free boundary hypersurfaces in the unit ball
• Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
• Inverse curvature flows in Riemannian warped products
• Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space
• The Minkowski inequality in de Sitter space
• The Gauss-Bonnet-Chern mass for graphic manifolds
• On an inverse curvature flow in two-dimensional space forms
• Note on Brendle-Eichmair's paper "Isoperimetric and Weingarten surfaces in the Schwarchild manifold"
• A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space
• Blaschke-Santaló type inequalities and quermassintegral inequalities in space forms
• Inverse curvature flow in anti-de Sitter-Schwarzschild manifold
• Isoperimetric inequalities for eigenvalues by inverse mean curvature flow
• Inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space ${\mathbb{R}}_1^{n+1}$
• Harmonic mean curvature flow and geometric inequalities
• Weighted Hsiung-Minkowski formulas and rigidity of umbilical hypersurfaces
• Geometric inequalities for hypersurfaces with nonnegative sectional curvature in hyperbolic space
• Inverse Gauss curvature flow in a time cone of Lorentz-Minkowski space ${\mathbb{R}}_1^{n+1}$
• Alexandrov-Fenchel type inequalities in the sphere
• Alexandrov-Fenchel type inequalities with convex weight in space forms
• Willmore inequality on hypersurfaces in hyperbolic space
• The GBC mass for asymptotically hyperbolic manifolds
• A Gauss curvature flow related to the Orlicz-Aleksandrov problem