Vol. 159, No. 1, 1993

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The standard double soap bubble in R2 uniquely minimizes perimeter

Joel Foisy, Manuel Alfaro Garcia, Jeffrey Farlowe Brock, Nickelous Hodges and Jason Zimba

Vol. 159 (1993), No. 1, 47–59
Abstract

Of course the circle is the least-perimeter way to enclose a region of prescribed area in the plane. This paper proves that a certain standard “double bubble” is the least-perimeter way to enclose and separate two regions of prescribed areas. The solution for three regions remains conjectural.

Mathematical Subject Classification 2000
Primary: 53A10
Secondary: 49Q05
Milestones
Received: 12 August 1991
Published: 1 May 1993
Authors
Joel Foisy
Department of Mathematics
SUNY Potsdam
44 Pierrepont Avenue
Potsdam NY 13676
United States
http://www2.potsdam.edu/foisyjs/
Manuel Alfaro Garcia
Jeffrey Farlowe Brock
Nickelous Hodges
Jason Zimba