Blaschke-Santal\'o type inequalities and quermassintegral inequalities in space forms
Differential Geometry
2025-10-08 v1
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-Santal\'o 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.
Keywords
Cite
@article{arxiv.2207.04281,
title = {Blaschke-Santal\'o type inequalities and quermassintegral inequalities in space forms},
author = {Yingxiang Hu and Haizhong Li},
journal= {arXiv preprint arXiv:2207.04281},
year = {2025}
}
Comments
23 pages, no figures. All comments are appreciated