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

Toroidal Soap Bubbles: Constant Mean Curvature Tori in S3S3 and R3 - Emma Carberry

Emma Carberry
University of Sydney
April 14, 2014
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.
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