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The double bubble problem on the flat two-torus

Author(s): Joseph Corneli; Paul Holt; George Lee; Nicholas Leger; Eric Schoenfeld; Benjamin Steinhurst
Journal: Trans. Amer. Math. Soc. 356 (2004), 3769-3820.
MSC (2000): Primary 53A10; Secondary 49Q10
Posted: March 12, 2004
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Abstract: We characterize the perimeter-minimizing double bubbles on all flat two-tori and, as corollaries, on the flat infinite cylinder and the flat infinite strip with free boundary. Specifically, we show that there are five distinct types of minimizers on flat two-tori, depending on the areas to be enclosed.

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Additional Information:

Joseph Corneli
Affiliation: C/O Frank Morgan, Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267 -- and -- Department of Mathematics, University of Texas, Austin, Texas 78712
Email: Frank.Morgan@williams.edu, jcorneli@math.utexas.edu

Paul Holt
Affiliation: Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267
Email: pholt@wso.williams.edu

George Lee
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Email: lee43@fas.harvard.edu

Nicholas Leger
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
Email: nickleger@mail.utexas.edu

Eric Schoenfeld
Affiliation: Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267
Email: eschoenf@wso.williams.edu

Benjamin Steinhurst
Affiliation: Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267
Email: Benjamin.A.Steinhurst@williams.edu

DOI: 10.1090/S0002-9947-04-03551-2
PII: S 0002-9947(04)03551-2
Received by editor(s): June 16, 2003
Posted: March 12, 2004
Copyright of article: Copyright 2004, American Mathematical Society

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