Current theme: Integrable systems
Mathematics
Soap bubbles: a gauge theory
byThomas Raujouan
Abstract: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.