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

Copyright 2000 Copyright 2000, Michael Hutchings, Frank Morgan, Manuel Ritoré, and Antonio Ros

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Article Info

• 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
• Comments (When Available)

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, Espańa

E-mail address: ritore@ugr.es

Antonio Ros

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

E-mail address: aros@ugr.es