The standard double soap bubble in ${\bf R}^2$ uniquely minimizes perimeter.
Manuel Alfaro, Jeffrey Brock, Joel Foisy, Nickelous Hodges, and Jason Zimba
Source: Pacific J. Math. Volume 159, Number 1
(1993), 47-59.
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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
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).
Mathematical Reviews (MathSciNet): MR54:8420
Zentralblatt MATH: 0327.49043
[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.
Mathematical Reviews (MathSciNet): MR89a:52036
Zentralblatt MATH: 0644.52002
[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).
Mathematical Reviews (MathSciNet): MR96a:58064
Zentralblatt MATH: 0925.53003
[Ta] Jean Taylor, The structure ofsingularities in soap-bubble-likeand soap-film-like minimal surfaces, Annals of Math., 103 (1976), 489-539.
Mathematical Reviews (MathSciNet): MR55:1208a
Zentralblatt MATH: 0335.49032
Pacific Journal of Mathematics
