Extremal spectral properties of Lawson tori

TL;DR

This paper investigates the extremal spectral properties of Lawson tori, showing that a specific eigenvalue of the Laplace-Beltrami operator is characterized by fundamental tones of associated Sturm-Liouville problems.

Contribution

It establishes a connection between eigenvalues of Lawson tori and fundamental tones of auxiliary Sturm-Liouville problems, providing a new spectral characterization.

Findings

Lawson tori have extremal metrics for certain Laplace-Beltrami eigenvalues.

Eigenvalues are expressed via fundamental tones of Sturm-Liouville problems.

The results link geometric spectral properties with classical differential equations.

Abstract

Extremal spectral properties of the Lawson tori are studied. A Lawson torus carries an extremal metric for some eigenvalue of the Laplace-Beltrami operator. The main result of this paper is that the number of this eigenvalue is expressed in terms of fundamental tones of auxiliary periodic Sturm-Liouville problems.