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.
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Darren King, Francesco Maggi, Salvatore Stuvard, Collapsing and the convex hull property in a soap film capillarity model. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 6, pp. 1929–1941DOI 10.1016/J.ANIHPC.2021.02.005