  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.
