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

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arxiv 2504.15109 v1 pith:ON2VULP2 submitted 2025-04-21 math.DG

Haizhong Li , Yong Wei , Botong Xu This is my paper · ORCID
classification math.DG
keywords curvaturedomainsheintze-karcherinequalitiesmanifoldsproductprovesub-static
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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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  1. On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds

    math.DG 2025-07 conditional novelty 6.0 of 10

    The authors establish that closed hypersurfaces satisfying certain constant shifted curvature equations in warped product manifolds are necessarily umbilic slices (or geodesic spheres in space forms), under conditions...

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