Tokyo Journal of Mathematics

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


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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.

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

First available in Project Euclid: 27 August 2008

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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.

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