On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products

Ning Zhang and Zhangsheng Zhu

Advances in Mathematical Physics, 2023, vol. 2023, issue 1

Abstract: We study constant mean curvature hypersurfaces constructed over the fiber Mn of warped products I×fMn. In this setting, assuming that the sign of the angle function does not changed along the hypersurfaces, we infer the uniqueness of such hypersurfaces by applying a parabolicity criterion. As an application, we get some Bernstein type theorems.

Date: 2023
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https://doi.org/10.1155/2023/6390463

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2023:y:2023:i:1:n:6390463

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