Collapsing and the convex hull property in a soap film capillarity model
arXiv:2002.06273 · doi:10.1016/j.anihpc.2021.02.005
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.
14 pages, 3 figures; in v3 we added some clarifications to Lemma 3.2
References in corpus (1)
Cited by in corpus (5)
- Smoothness of collapsed regions in a capillarity model for soap films
- Plateau's problem as a singular limit of capillarity problems
- An existence theorem for Brakke flow with fixed boundary conditions
- On the relaxation of Gauss's capillarity theory under spanning conditions
- Regularity for Minimizers of a Planar Partitioning Problem with Cusps