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arXiv · 2504.15109

New Heintze-Karcher type inequalities in sub-static warped product manifolds

Haizhong Li·Yong Wei·Botong Xu
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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.

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Haizhong Li, Yong Wei, Botong Xu. 2025-04-21. New Heintze-Karcher type inequalities in sub-static warped product manifolds. https://arxiv.org/abs/2504.15109

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