Séminaire de Physique Théorique

Dynamic Interconversions of Minimal Surfaces

by Prof. Raymond GOLDSTEIN (University of Cambridge & IHES)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


35, route de Chartres, F-91440 Bures-sur-Yvette (France)

A classical problem in mathematics is the determination of the minimal surface that spans a given contour, which can be realized in the laboratory as a soap film supported by a wire frame. In the early 1940s Richard Courant pointed out nontrivial situations in which a small deformation of certain frames can render unstable the supported surface, leading by a rapid dynamical process to a new minimal surface. For example, a soap film Möbius strip can transition to a disc. Despite the enormous body of work on the mathematics of minimal surfaces themselves, the understanding of these dynamical problems is at a very early stage. In this talk I will summarize our recent experimental and theoretical work on problems of this type, in which a combination of high-speed imaging and stability theory has revealed new insights. (Work done in collaboration with A.I. Pesci, H.K. Moffatt, T. Machon and G.P. Alexander)