A capillarity model for soap films

Abstract: We model soap films, rather than as two dimensional surfaces with vanishing mean curvature, as three dimensional objects with small volume. Surface energy minimization then leads, at least heuristically, either to observe objects with small thickness, or minimal surfaces with multiplicity two joined by regions of high negative curvature bounding the given volume. We report on the various results known on this model and to the many questions left open. This is based on joint papers with Darren King (NYU), Salvatore Stuvard (Milano Statale) and Antonello Scardicchio (ICTP Trieste)