JournalsaihpcVol. 38, No. 6pp. 1929–1941

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

  • Darren King

    Department of Mathematics, The University of Texas at Austin, 2515 Speedway, Stop C1200, Austin TX 78712-1202, USA

  • Francesco Maggi

    Department of Mathematics, The University of Texas at Austin, 2515 Speedway, Stop C1200, Austin TX 78712-1202, USA

  • Salvatore Stuvard

    Department of Mathematics, The University of Texas at Austin, 2515 Speedway, Stop C1200, Austin TX 78712-1202, USA
Collapsing and the convex hull property in a soap film capillarity model cover

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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.

Cite this article

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. 1929–1941

DOI 10.1016/J.ANIHPC.2021.02.005