## Tokyo Journal of Mathematics

### The spectra of Jacobi operators for Constant Mean Curvature Tori of Revolution in the $3$-sphere

#### Abstract

We prove a theorem about elliptic operators with symmetric potential functions, defined on a function space over a closed loop. The result is similar to a known result for a function space on an interval with Dirichlet boundary conditions. These theorems provide accurate numerical methods for finding the spectra of those operators over either type of function space. As an application, we numerically compute the Morse index of constant mean curvature tori of revolution in the unit $3$-sphere $\mathbb{S}^3$, confirming that every such torus has Morse index at least five, and showing that other known lower bounds for this Morse index are close to optimal.

#### Article information

Source
Tokyo J. Math., Volume 31, Number 1 (2008), 161-174.

Dates
First available in Project Euclid: 27 August 2008

https://projecteuclid.org/euclid.tjm/1219844829

Digital Object Identifier
doi:10.3836/tjm/1219844829

Mathematical Reviews number (MathSciNet)
MR2426800

Zentralblatt MATH identifier
1152.58003

#### Citation

ROSSMAN, Wayne; SULTANA, Nahid. The spectra of Jacobi operators for Constant Mean Curvature Tori of Revolution in the $3$-sphere. Tokyo J. Math. 31 (2008), no. 1, 161--174. doi:10.3836/tjm/1219844829. https://projecteuclid.org/euclid.tjm/1219844829

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