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

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  • Ning Zhang
  • Zhangsheng Zhu
  • Mohammad W. Alomari

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.

Suggested Citation

  • Ning Zhang & Zhangsheng Zhu & Mohammad W. Alomari, 2023. "On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products," Advances in Mathematical Physics, Hindawi, vol. 2023, pages 1-6, June.
    • Handle: RePEc:hin:jnlamp:6390463
    DOI: 10.1155/2023/6390463
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