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The double bubble conjecture


Authors: Joel Hass, Michael Hutchings and Roger Schlafly
Journal: Electron. Res. Announc. Amer. Math. Soc. 1 (1995), 98-102
MSC (1991): Primary 53A10, 49Q10, 49Q25
DOI: https://doi.org/10.1090/S1079-6762-95-03001-0
Comment: Additional information about this paper
MathSciNet review: 1369639
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Abstract | References | Similar Articles | Additional Information

Abstract: The classical isoperimetric inequality states that the surface of smallest area enclosing a given volume in $R^3$ is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of $2 \pi / 3$.


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  • 1 M. Alfaro, J. Brock, J. Foisy, N. Hodges and J. Zimba The standard double soap bubble in $ R^2$ uniquely minimizes perimeter, Pac. J. Math. 159, 47-59 (1993). MR 94b:53019
  • 2 F.J. Almgren, Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, Memoirs Amer. Math. Soc. 4, 165-199 (1976). MR 54:8420
  • 3 F.J. Almgren and J. Taylor, The geometry of soap films and soap bubbles, Sci. Amer. 235,82-93 (1976).
  • 4 ANSI/IEEE Standard 754-1985 for Binary Floating-Point Arithmetic, The Institute of Electrical and Electronic Engineers, New York, 1985.
  • 5 C.V. Boys, Soap Bubbles, Dover Publ. Inc. NY 1959 (first edition 1911).
  • 6 C. Delaunay, Sur la surface de revolution dont la courbure moyenne est constante, J. Math. Pure et App. 16, 309-321 (1841).
  • 7 J. Eells, The surfaces of Delaunay, Math. Intelligencer 9, 53-57 (1987). MR 88h:53011
  • 8 J. Foisy, Soap bubble clusters in $R^2$ and $R^3$, undergraduate thesis, Williams College (1991).
  • 9 J. Hass and R. Schlafly, Double Bubbles Minimize, (preprint).
  • 10 M. Hutchings, The structure of area-minimizing double bubbles, to appear in J. Geom. Anal.
  • 11 F. Morgan, Clusters minimizing area plus length of singular curves, Math. Ann. 299, 697-714 (1994). MR 95g:49083
  • 12 R. E. Moore, Methods and Applications of Interval Analysis, SIAM, 1979. MR 81b:65040
  • 13 J. Plateau, Statique expérimentale et théorique des liquides soumis aux seules forces moleculaires, Gathier-Villars, Paris, 1873.
  • 14 J. Taylor, The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces, Ann. of Math. 103, 489-539 (1976). MR 55:1208a
  • 15 D'arcy Thompson, On growth and form, Cambridge Univ. Press, NY, 1959, (first edition 1917). MR 23:B1601

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Additional Information

Joel Hass
Affiliation: Department of Mathematics, University of California, Davis, CA 95616
Email: hass@math.ucdavis.edu

Michael Hutchings
Affiliation: Department of Mathematics, Harvard University, Cambridge, MA 02138
Email: hutching@math.harvard.edu

Roger Schlafly
Affiliation: Real Software, PO Box 1680, Soquel, CA 95073
Email: rschlafly@attmail.com

DOI: https://doi.org/10.1090/S1079-6762-95-03001-0
Keywords: Double bubble; isoperimetric
Received by editor(s): September 11, 1995
Additional Notes: Hass was partially supported by the NSF
Hutchings was supported by an NSF Graduate Fellowship.
Communicated by: Richard Schoen
Article copyright: © Copyright 1996 Hass, Hutchings, Schlafly

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