Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space

Abstract

In this paper, we solve various isoperimetric problems for the quermassintegrals and the curvature integrals in the hyperbolic space $\H^n$, by using quermassintegral preserving curvature flows. As a byproduct, we obtain hyperbolic Alexandrov-Fenchel inequalities.

20 pages

References in corpus (4)

• A geometric inequality on hypersurface in hyperbolic space
• A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold
• Mixed volume preserving curvature flows in hyperbolic space
• Rigidity for nearly umbilical hypersurfaces in space forms

Cited by in corpus (8)

• Locally constrained inverse curvature flows
• Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball
• Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
• The Gauss-Bonnet-Chern mass for graphic manifolds
• Mixed volume preserving curvature flows in hyperbolic space
• Penrose inequalities and a positive mass theorem for charged black holes in higher dimension
• Volume preserving Gauss curvature flow of convex hypersurfaces in the hyperbolic space
• The GBC mass for asymptotically hyperbolic manifolds