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

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

2008-09-06

arxiv.org/abs/0809.1173v2

The Journal of Geometric Analysis, v. 20, p. 63-71, 2010.

Mathematics

Differential Geometry

This article is an improvement of an earlier version titled On the spectrum of Martin-Morales minimal surfaces. 7 pages

Scientific paper

10.1007/s12220-009-9101-z

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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