Collapsing and the convex hull property in a soap film capillarity model
King, Darren1 ; Maggi, Francesco1 ; Stuvard, Salvatore1
1 Department of Mathematics, The University of Texas at Austin, 2515 Speedway, Stop C1200, Austin TX 78712-1202, USA
Annales de l'I.H.P. Analyse non linéaire, novembre – décembre 2021, Tome 38 (2021) no. 6, pp. 1929-1941.
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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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Révisé le :
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DOI : 10.1016/j.anihpc.2021.02.005
Classification : 49Q05, 53A10, 49Q20
Mots-clés : Convex hull property, Minimal surfaces, Constant mean curvature surfaces, Plateau's problem
King, Darren 1 ; Maggi, Francesco 1 ; Stuvard, Salvatore 1

1 Department of Mathematics, The University of Texas at Austin, 2515 Speedway, Stop C1200, Austin TX 78712-1202, USA 
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King, Darren; Maggi, Francesco; Stuvard, Salvatore. Collapsing and the convex hull property in a soap film capillarity model. Annales de l'I.H.P. Analyse non linéaire, novembre – décembre 2021, Tome 38 (2021) no. 6, pp. 1929-1941. doi : 10.1016/j.anihpc.2021.02.005. http://www.numdam.org/articles/10.1016/j.anihpc.2021.02.005/

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