A new bound on the Morse index of constant mean curvature tori of revolution in $\mathbb{S}^3$

TL;DR

This paper establishes a new lower bound on the Morse index for constant mean curvature tori of revolution in the three-sphere by explicitly calculating negative eigenvalues of the Jacobi operator.

Contribution

It introduces a novel method to estimate the Morse index by explicitly computing eigenvalues for this class of surfaces.

Findings

New lower bound on the Morse index for these tori

Explicit computation of negative eigenvalues of the Jacobi operator

Enhanced understanding of stability properties of CMC tori in $\

Abstract

In this work we give a new lower bound on the Morse index for constant mean curvature tori of revolution immersed in the three-sphere $\mathbb{S}^3$, by computing some explicit negative eigenvalues for the corresponding Jacobi operator.