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.

Collapsing and the convex hull property in a soap film capillarity model / D. King, F. Maggi, S. Stuvard. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 38:6(2021 Nov), pp. 1929-1941. [10.1016/j.anihpc.2021.02.005]

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

S. Stuvard
2021

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.
convex hull property; minimal surfaces; Plateau's problem
Settore MAT/05 - Analisi Matematica
nov-2021
15-feb-2021
Article (author)
File in questo prodotto:
File Dimensione Formato  
Collapsing and the convex hull property in a soap film capillarity model (w: King and Maggi).pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 358.87 kB
Formato Adobe PDF
358.87 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
2002.06273.pdf

accesso aperto

Tipologia: Pre-print (manoscritto inviato all'editore)
Dimensione 191.92 kB
Formato Adobe PDF
191.92 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/850383
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 4
social impact