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Geometriae Dedicata

, Volume 156, Issue 1, pp 31–47 | Cite as

An estimate for the scalar curvature of constant mean curvature hypersurfaces in space forms

  • Luis J. Alías
  • S. Carolina García-Martínez
Original Paper

Abstract

In this paper we derive a sharp estimate for the supremum of the scalar curvature (or, equivalently, the infimum of the squared norm of the second fundamental form) of a constant mean curvature hypersurface with two principal curvatures immersed into a Riemannian space form of constant curvature. Our results will be an application of the generalized Omori-Yau maximum principle, following the approach by Pigola et al. (Memoirs Am Math Soc 822, 2005).

Keywords

Constant mean curvature Scalar curvature Ricci curvature Second fundamental form Omori-Yau maximum principle 

Mathematics Subject Classification (2000)

53C40 53C42 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Luis J. Alías
    • 1
  • S. Carolina García-Martínez
    • 1
  1. 1.Departamento de MatemáticasUniversidad de MurciaEspinardo, MurciaSpain

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