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Uniqueness of hypersurfaces in weighted product spaces via maximum principles for the drift Laplacian

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Abstract

We apply suitable maximum principles for the drift Laplacian to obtain several uniqueness results concerning complete two-sided hypersurfaces immersed with constant f-mean curvature in a weighted product space of form \({\mathbb {R}}\times M_{f}^{n}\) and such that its potential function f does not depend on the parameter \(t\in {\mathbb {R}}\). Among these results, we prove that the slices are the only complete two-sided f-minimal hypersurfaces lying in a half-space of \({\mathbb {R}}\times M_{f}^{n}\) and such that the Bakry–Émeri–Ricci tensor is bounded from below. Furthermore, we study the f-mean curvature equation related to entire graphs defined on the base \(M^{n}\).

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Acknowledgements

The authors would like to thank the referee for his/her valuable suggestions and useful comments which improved the paper.

Funding

The first author is partially supported by CAPES, Brazil. The second and third authors are partially supported by CNPq, Brazil, grants 309668/2021-2 and 301970/2019-0, respectively.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal da Paraíba, 58051-900, João Pessoa, Paraíba, Brazil

    Danilo F. da Silva & Eraldo A. Lima Jr

  2. Departamento de Matemática, Universidade Federal de Campina Grande, 58429-970, Campina Grande, Paraíba, Brazil

    Henrique F. de Lima

Authors
  1. Danilo F. da Silva
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  2. Eraldo A. Lima Jr
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  3. Henrique F. de Lima
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Correspondence to Henrique F. de Lima.

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da Silva, D.F., Lima, E.A. & de Lima, H.F. Uniqueness of hypersurfaces in weighted product spaces via maximum principles for the drift Laplacian. Boll Unione Mat Ital 16, 507–520 (2023). https://doi.org/10.1007/s40574-022-00337-5

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  • DOI: https://doi.org/10.1007/s40574-022-00337-5

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