Stable hypersurfaces via the first eigenvalue of the anisotropic Laplacian operator

  • Jonatan Floriano da Silva
  • Henrique Fernandes de Lima
  • Marco Antonio Lázaro Velásquez


In this paper we provide a characterization for stable hypersurfaces with constant anisotropic mean curvature immersed in the Euclidean space \(\mathbb {R}^{n+1}\) through the analysis of the first eigenvalue of the anisotropic Laplacian operator.


Euclidean space Wulff shape Anisotropic mean curvatures \((r, s, F)\)-linear Weingarten surfaces Stable closed hypersurfaces Jacobi operator 

Mathematics Subject Classification

Primary 53C42 Secondary 53B25 



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


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Copyright information

© Università degli Studi di Ferrara 2018

Authors and Affiliations

  • Jonatan Floriano da Silva
    • 1
  • Henrique Fernandes de Lima
    • 2
  • Marco Antonio Lázaro Velásquez
    • 2
  1. 1.Departamento de MatemáticaUniversidade Federal do CearáFortalezaBrazil
  2. 2.Departamento de MatemáticaUniversidade Federal de Campina GrandeCampina GrandeBrazil

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