, Volume 20, Issue 1, pp 63-71
Date: 07 Aug 2009

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

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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).

The first and third author were partially supported by CNPq-CAPES, Brazil.