English

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