[HM] Double Bubble Conjecture Proved

Subject: [HM] Double Bubble Conjecture Proved
From: Antreas P. Hatzipolakis (xpolakis@otenet.gr)
Date: Sat Mar 18 2000 - 12:21:54 EST

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Research Announcement, February 25, 2000

Proof of the Double Bubble Conjecture

by Michael Hutchings, Frank Morgan, Manuel Ritore, and Antonio Ros

<quote>
History. Archimedes and Zenodorus (see [K, p. 273]) claimed and Schwarz
[S] proved that the round sphere is the least-perimeter way to enclose a
given volume in R3. The Double Bubble Conjecture, long assumed true (see
[P, pp. 300-301], [B, p. 120]) but only recently stated as a conjecture [F1,
sect. 3], says that the familiar double soap bubble on the right in Figure 1,
consisting of two spherical caps separated by a spherical cap or flat disc,
meeting at 120-degree angles, provides the least-perimeter way to
enclose and separate two given volumes. The analogous result in R2 was
proved by the 1990 Williams College "SMALL" undergraduate research
Geometry Group [F2]. In 1995, Hass, Hutchings, and Schlafly [HHS]
announced a computer-assisted proof for the case of equal volumes in R3.
(See [M1], [HS1], [HS2], [Hu], [M2, chapt. 13].) Here we announce a proof
[HMRR] of the general Double Bubble Conjecture in R3, using stability
arguments.
</quote>

http://www.williams.edu/Mathematics/fmorgan/ann.html