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Strongly Stable Linear Weingarten Hypersurfaces Immersed in the Hyperbolic Space

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Abstract

In this article, we establish the notion of strong stability related to closed linear Weingarten hypersurfaces immersed in the hyperbolic space. In this setting, initially we show that geodesic spheres are strongly stable. Afterwards, under a suitable restriction on the mean and scalar curvatures, we prove that if a closed linear Weingarten hypersurface into the hyperbolic space is strongly stable, then it must be a geodesic sphere, provided that the image of its Gauss mapping is contained in a chronological future (or past) of the de Sitter space.

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Authors and Affiliations

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

    Henrique F. de. Lima & Marco Antonio L. Velásquez

  2. Departamento de Matemática, Universidade Federal de Pernambuco, Recife, Pernambuco, 50740-560, Brazil

    Antonio F. de. Sousa

Authors
  1. Henrique F. de. Lima
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  2. Antonio F. de. Sousa
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  3. Marco Antonio L. Velásquez
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Corresponding author

Correspondence to Henrique F. de. Lima.

Additional information

This work was started when de Sousa was visiting the Mathematics Departament of the Universidade Federal de Campina Grande, with financial support from CAPES, Brazil. He would like to thank this institution for its hospitality. de Lima is partially supported by CNPq, Brazil, Grant 300769/2012-1. Velásquez was partially supported by CNPq, Brazil, Grant 552.464/2011-2. The authors would like to thank the referee for giving valuable suggestions which improved the paper.

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de. Lima, H.F., de. Sousa, A.F. & Velásquez, M.A.L. Strongly Stable Linear Weingarten Hypersurfaces Immersed in the Hyperbolic Space. Mediterr. J. Math. 13, 2147–2160 (2016). https://doi.org/10.1007/s00009-015-0600-9

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  • DOI: https://doi.org/10.1007/s00009-015-0600-9

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