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International Journal of Mathematics and Mathematical Sciences
Volume 32, Issue 11, Pages 641-699
http://dx.doi.org/10.1155/S0161171202207188

The double bubble problem in spherical and hyperbolic space

1Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA
2Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK

Received 28 July 2002

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove that the standard double bubble is the least-area way to enclose and separate two regions of equal volume in 3, and in S3 when the exterior is at least ten percent of S3.