Geometriae Dedicata

, Volume 162, Issue 1, pp 345–362 | Cite as

Good candidates for least area soap films

Original Paper


Soap films are presented as potential global area minimizers subject to a topological constraint. Experimentally, this constraint is the shape of the soapy water in a soap film experiment. In this context, soap films which are probable area minimizers for rectangular n-prisms are described. By allowing area minimizers which arise as deformations of higher genus surfaces, we are able to discover previously unknown soap films spanning rectangular n-prisms with large aspect ratios and n ≥ 5. For n = 3, 4, 5, we show that the central film contracts to a point as the aspect ratio of the prism increases. We also prove that the area of the central hexagon for a soap film spanning a tall 6-prism approaches zero like (height)−4 as the height approaches infinity, provided we fix the length of the hexagon base. Finally, we prove that, if the aspect ratio is large enough, the soap film produced experimentally spanning a 4-prism has films which look planar but in reality are non-planar.


Soap film Experiment Least area Rectangular prism 

Mathematics Subject Classification

Primary 49Q05 Secondary 51M04 


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  1. 1.
    Almgren, F.J. Jr.: Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints. Mem. AMS No. 165 (1976)Google Scholar
  2. 2.
    Almgren F.J., Taylor J.E.: The geometry of soap films and soap bubbles. Sci. Am. 235(1), 82–93 (1976)CrossRefGoogle Scholar
  3. 3.
    Cox S.J., Hutzler S., Janiaud E., Van der Net A., Weaire D.: Pre-empting plateau: the nature of topological transitions in foam. Europhys. Lett. 77, 28002 (2007)CrossRefGoogle Scholar
  4. 4.
    Cox S.J., Hutzler S., Saadatfar M., Van der Net A., Weaire D.: The dynamics of a topological change in a system of soap films. Coll. Surf. A 323, 123–131 (2008)CrossRefGoogle Scholar
  5. 5.
    Huff R.: Soap films spanning rectangular prisms. Geom. Dedicata 123(1), 223–238 (2006)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Huff R.: An immersed soap film of genus one. Comm. Anal. Geom. 19(3), 601–631 (2011)MathSciNetMATHGoogle Scholar
  7. 7.
    Taylor J.: The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces. Ann. Math. 103, 489–539 (1976)MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of MathematicsHarding UniversitySearcyUSA

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