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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The standard double bubble is the unique stable double bubble in $\mathbf{R}^2$


Authors: Frank Morgan and Wacharin Wichiramala
Journal: Proc. Amer. Math. Soc. 130 (2002), 2745-2751
MSC (2000): Primary 53A10, 49Q20, 53Cxx
Published electronically: April 17, 2002
MathSciNet review: 1900881
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Abstract: We prove that the only equilibrium double bubble in $\mathbf{R}^2$ which is stable for fixed areas is the standard double bubble. This uniqueness result also holds for small stable double bubbles in surfaces, where it is new even for perimeter-minimizing double bubbles.


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Additional Information

Frank Morgan
Affiliation: Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267
Email: Frank.Morgan@williams.edu

Wacharin Wichiramala
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Email: wichiram@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06640-6
PII: S 0002-9939(02)06640-6
Keywords: Stable double bubble, standard double bubble, soap bubble
Received by editor(s): April 18, 2001
Published electronically: April 17, 2002
Communicated by: Bennett Chow
Article copyright: © Copyright 2002 by the authors