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New
Heintze–Karcher-type inequalities in substatic warped product
manifolds
Haizhong Li, Yong Wei and Botong Xu |
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Vol. 345 (2026), No. 1, 105–126
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Abstract |
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We establish Heintze–Karcher-type inequalities involving the shifted mean curvature for smooth bounded domains in certain substatic warped product manifolds. In particular, we prove a novel Heintze–Karcher-type inequality for horospherical mean concave domains in the hyperbolic space. We apply these results to derive uniqueness theorems for hypersurfaces satisfying a class of curvature equations. |
Keywords
Heintze–Karcher inequality, shifted principal curvatures,
unit normal flow, substatic manifold
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Mathematical Subject Classification
Primary: 53C24, 53C42
Secondary: 53C21
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Milestones
Received: 9 August 2025
Revised: 1 April 2026
Accepted: 17 July 2026
Published: 25 September 2026
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Authors |
| Haizhong Li | |
| Department of Mathematical
Sciences Tsinghua University Beijing China |
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| Yong Wei | |
| School of Mathematical
Sciences University of Science and Technology of China Hefei China |
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| Botong Xu | |
| Department of Mathematics Technion-Israel Institute of Technology Haifa Israel |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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