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

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.

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

References in corpus (3)

• The mean curvature of cylindrically bounded submanifolds
• Discreteness of the spectrum of the Laplace-Beltrami operator
• On the spectrum of $\bar{X}$-bounded minimal submanifolds

Cited by in corpus (5)

• On the spectrum of bounded immersions
• A barrier principle at infinity for varifolds with bounded mean curvature
• On the Spectrum of Certain Hadamard Manifolds
• A Spectral Bernstein Theorem
• Spectrum of the Laplacian on radial graphs