## Toroidal Soap Bubbles: Constant Mean Curvature Tori in \(S^3\) and \(R^3\)

Emma Carberry (Sydney)

Abstract

Constant mean curvature (CMC) tori in \(S^3\), \(R^3\) or \(H^3\) are in bijective correspondence with spectral curve data, consisting of a hyperelliptic curve, a line bundle on this curve and some additional data, which in particular determines the relevant space form. This point of view is particularly relevant for considering moduli-space questions, such as the prevalence of tori amongst CMC planes and whether tori can be deformed. I will address these questions for the spherical and Euclidean cases, using Whitham deformations.