Pacific Journal of Mathematics

The standard double soap bubble in ${\bf R}^2$ uniquely minimizes perimeter.

Manuel Alfaro, Jeffrey Brock, Joel Foisy, Nickelous Hodges, and Jason Zimba

Article information

Source
Pacific J. Math. Volume 159, Number 1 (1993), 47-59.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
http://projecteuclid.org/euclid.pjm/1102634378

Zentralblatt MATH identifier
0782.49026

Zentralblatt MATH identifier
0738.49023

Mathematical Reviews number (MathSciNet)
MR1211384

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 49Q05: Minimal surfaces [See also 53A10, 58E12]

Citation

Foisy, Joel; Alfaro, Manuel; Brock, Jeffrey; Hodges, Nickelous; Zimba, Jason. The standard double soap bubble in ${\bf R}^2$ uniquely minimizes perimeter. Pacific J. Math. 159 (1993), no. 1, 47--59. http://projecteuclid.org/euclid.pjm/1102634378.


Export citation

References

  • [A] Manuel Alfaro, Jeffrey Brock, Joel Foisy, Nickelous Hodges, and Jason Zimba, Compound soap bubbles in theplane, SMALL undergraduate research project, Williams College, 1990.
  • [Al] F. J. Almgren, Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, Mem. Amer. Math. Soc, 35 (1976).
  • [ATa] F. J. Almgren, Jr. and J. E. Taylor, The geometry of soap films and soap bubbles, Scientific American, July 1976, 82-93.
  • [B] Michael H. Bleicher, Isoperimetric division into a finite number of cells in the plane, Studia Sci. Math. Hung., 22 (1987), 123-137.
  • [F] Joel Foisy, Soap Bubble Clusters in R2 and R3, Senior Honors Thesis, Williams College, 1991.
  • [M] Frank Morgan, Soap bubbles in R2 and in surfaces, preprint (1992).
  • [Ta] Jean Taylor, The structure ofsingularities in soap-bubble-likeand soap-film-like minimal surfaces, Annals of Math., 103 (1976), 489-539.