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

Members' Seminar
Topic:Toroidal Soap Bubbles: Constant Mean Curvature Tori in \(S^3\) and \(R^3\)
Speaker:Emma Carberry
Affiliation:University of Sydney
Date:Monday, April 14
Time/Room:2:00pm - 3:00pm/S-101
Video Link:http://video.ias.edu/members/2014/0414-EmmaCarberry

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. I will address these periodicity questions for the spherical and Euclidean cases, using Whitham deformations, which I will explain.