Blaschke-Santaló type inequalities and quermassintegral inequalities in space forms

Abstract

In this paper, we prove a family of identities for closed and strictly convex hypersurfaces in the sphere and hyperbolic/de Sitter space. As applications, we prove Blaschke-Santaló type inequalities in the sphere and hyperbolic/de Sitter space, which generalizes the previous work of Gao, Hug and Schneider \cite{GHS03}. We also prove the quermassintegral inequalities in hyperbolic/de Sitter space.

arXiv comment23 pages, no figures. All comments are appreciated

References in corpus (10)

• A geometric inequality on hypersurface in hyperbolic space
• Volume preserving flow and Alexandrov-Fenchel type inequalities in hyperbolic space
• Curvature flows in the sphere
• Locally constrained curvature flows and geometric inequalities in hyperbolic space
• Rigidity results, inverse curvature flows and Alexandrov-Fenchel type inequalities in the sphere
• A fully-nonlinear flow and quermassintegral inequalities in the sphere
• Alexandrov-Fenchel type inequalities for convex hypersurfaces in hyperbolic space and in sphere
• Isoperimetric problems for spacelike domains in generalized Robertson-Walker spaces
• The Minkowski inequality in de Sitter space
• Harnack inequalities for curvature flows in Riemannian and Lorentzian manifolds