Proof of the double bubble conjecture

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Abstract.

We prove that the standard double bubble provides the least-area way to enclose and separate two regions of prescribed volume in ${\mathbb R}^3$.

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ERA Amer. Math. Soc. 06 (2000), pp. 45-49
Publisher Identifier: S 1079-6762(00)00079-2
2000 Mathematics Subject Classification. Primary 53A10; Secondary 53C42
Key words and phrases. Double bubble, soap bubbles, isoperimetric problems, stability
Received by the editors March 3, 2000
Posted on July 17, 2000
Communicated by Richard Schoen
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Michael Hutchings

Department of Mathematics, Stanford University, Stanford, CA 94305

E-mail address: hutching@math.stanford.edu

Frank Morgan

Department of Mathematics, Williams College, Williamstown, MA 01267

E-mail address: Frank.Morgan@williams.edu

Manuel Ritoré

Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, España

E-mail address: ritore@ugr.es

Antonio Ros

Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, España

E-mail address: aros@ugr.es