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

DOI: 10.2140/pjm.1993.159.47

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