Soap bubbles: a gauge theory

par Dr Thomas Raujouan (Institut für Differentialgeometrie, University of Hanover, Germany)

mardi 15 mars 2022, 14:00 → 15:00 Europe/Paris

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Constant Mean Curvature (CMC) surfaces are mathematical models for soap films, with or without volume constraints. The equations governing them form an integrable system which can be formulated in a gauge theoretic point of view. This formulation leads to a generalized holomorphic representation for CMC surfaces in Euclidean, Spherical and Hyperbolic three-spaces, which allows for the construction of new surfaces, together with the computation of their areas and proofs of their embeddedness.

 

Keywords

Minimal and CMC surfaces, integrable systems, Riemann surfaces.