Collapsing and the convex hull property in a soap film capillarity model

Soap films hanging from a wire frame are studied in the framework of capillarity 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. (C) 2021 L'Association Publications de l'Institut Henri Poincare. Published by Elsevier B.V. All rights reserved.