New Heintze-Karcher type inequalities in sub-static warped product manifolds
Differential Geometry
2025-04-22 v1
Abstract
In this paper, we prove Heintze-Karcher type inequalities involving the shifted mean curvature for smooth bounded domains in certain sub-static warped product manifolds. In particular, we prove a Heintze-Karcher-type inequality for non mean-convex domains in the hyperbolic space. As applications, we obtain uniqueness results for hypersurfaces satisfying a class of curvature equations.
Keywords
Cite
@article{arxiv.2504.15109,
title = {New Heintze-Karcher type inequalities in sub-static warped product manifolds},
author = {Haizhong Li and Yong Wei and Botong Xu},
journal= {arXiv preprint arXiv:2504.15109},
year = {2025}
}
Comments
18 pages. Comments are welcome