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arXiv · 0809.1173

On the essential spectrum of Nadirashvili-Martin-Morales minimal surfaces

G. Pacelli Bessa·Luquesio P. Jorge·J. Fabio Montenegro
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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 $\mathbb{R}^{3}$ is discrete. This gives a positive answer to a question of Yau.

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G. Pacelli Bessa, Luquesio P. Jorge, J. Fabio Montenegro. 2008-09-06. On the essential spectrum of Nadirashvili-Martin-Morales minimal surfaces. https://doi.org/10.1007/s12220-009-9101-z

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