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arXiv · 2002.06273

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

Darren King·Francesco Maggi·Salvatore Stuvard
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Abstract

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. 2020-02-14. Collapsing and the convex hull property in a soap film capillarity model. https://doi.org/10.1016/j.anihpc.2021.02.005

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