ncts

The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a soap film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. We establish the existence of an equilibrium shape that minimizes the total potential energy of the system under the physical constraint of non-interpenetration of matter, but allowing for self-contact of the filament. In our treatment, the bounding filament retains a finite thickness and, thus, a nonvanishing volume, while the soap film is represented by a set with finite two-dimensional Hausdorff measure. Moreover,the region of contact between the soap film and the surface of the filament is not prescribed a priori. This is joint work with Giulio Giusteri and Luca Lussardi.