Stability of Hypersurfaces with Constant Mean Curvature

  • João Lucas Barbosa
  • Manfredo do Carmo
Chapter

Abstract

Let \(x:{\text M}^{n}\rightarrow\,{\text R}^{n+1}\) be an immersion of an orientable, n-dimensional manifold \({\text M}^{n}\) into the euclidean space \({\text R}^{n+1}\). The condition that x has nonzero constant mean curvature H = H 0 is known to be equivalent to the fact that xis a critical point of a variational problem.

Keywords

Variation Vector Jacobi Equation Rotation Surface Compact Domain Cylindrical Domain 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • João Lucas Barbosa
    • 1
  • Manfredo do Carmo
    • 2
  1. 1.Departamento de MatemáticaUniversidade Federal do CearáFortalezaBrasil
  2. 2.Instituto de Matemática Pura e AplicadaRio de JaneiroBrasil

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