Calculus of Variations and Geometric Measure Theory

D. King - F. Maggi - S. Stuvard

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

created by maggi on 14 Feb 2020
modified by stuvard on 16 Jan 2022


Published Paper

Inserted: 14 feb 2020
Last Updated: 16 jan 2022

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Volume: 38
Number: 6
Pages: 1929-1941
Year: 2021
Doi: 10.1016/j.anihpc.2021.02.005

ArXiv: 2002.06273 PDF
Links: ANIHP


Soap films hanging from a wire frame are studied in the framework of capil- larity 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.