The University of Sydney - School of Mathematics and Statistics

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.