Inserted: 14 feb 2020
Last Updated: 19 feb 2021
Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Soap films hanging from a wire frame are studied in the framework of capil- larity theory. Minimizers in the corresponding variational problem are known to consist of positive volume regions with boundaries of constant mean curvature (pressure), possibly connected by "collapsed" minimal surfaces. We prove here that collapsing only occurs if the mean curvature (pressure) of the bulky regions is negative, and that, when this last property holds, the whole soap film lies in the convex hull of its boundary wire frame.