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The double bubble conjecture
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## The double bubble conjecture

### Joel Hass, Michael Hutchings, and Roger Schlafly

**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 $2 \pi / 3$.

*Copyright Hass, Hutchings, Schlafly 1996*

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#### Article Info

- ERA Amer. Math. Soc.
**01** (1995), pp. 98-102
- Publisher Identifier: S1079-6762(95)03001-0
- 1991
*Mathematics Subject Classification*. Primary 53A10; Secondary 49Q10, 49Q25.
*Key words and phrases*. Double bubble; isoperimetric
- Received by the editors September 11, 1995
- Communicated by Richard Schoen
- Comments

**Joel Hass**

Department of Mathematics,
University of California, Davis, CA 95616

*E-mail address:* `hass@math.ucdavis.edu`

**Michael Hutchings**

Department of Mathematics, Harvard University, Cambridge, MA 02138

*E-mail address:* `hutching@math.harvard.edu`

** Roger Schlafly **

Real Software, PO Box 1680,
Soquel, CA 95073

*E-mail address:* `rschlafly@attmail.com`

Hutchings was supported by an NSF Graduate Fellowship

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