Journal of Geometric Analysis

, Volume 20, Issue 1, pp 63–71 | Cite as

The Spectrum of the Martin-Morales-Nadirashvili Minimal Surfaces Is Discrete

  • G. Pacelli Bessa
  • Luquesio P. Jorge
  • J. Fabio Montenegro
Article

Abstract

We show that the spectrum of a complete submanifold properly immersed into a ball of a Riemannian manifold is discrete, provided the norm of the mean curvature vector is sufficiently small. In particular, the spectrum of a complete minimal surface properly immersed into a ball of ℝ3 is discrete. This gives a positive answer to a question of Yau (Asian J. Math. 4:235–278, 2000).

Keywords

Proper bounded minimal submanifolds Discrete spectrum Essential spectrum 

Mathematics Subject Classification (2000)

53C40 53C42 58C40 

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Copyright information

© Mathematica Josephina, Inc. 2009

Authors and Affiliations

  • G. Pacelli Bessa
    • 1
  • Luquesio P. Jorge
    • 1
  • J. Fabio Montenegro
    • 1
  1. 1.Department of MathematicsUniversidade Federal do Ceara–UFCFortalezaBrazil

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