The Spectrum of the Martin-Morales-Nadirashvili Minimal Surfaces Is Discrete |
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Authors: | G. Pacelli Bessa Luquesio P. Jorge J. Fabio Montenegro |
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Affiliation: | 1.Department of Mathematics,Universidade Federal do Ceara–UFC,Fortaleza,Brazil |
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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). |
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