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Two partial Spheres with a separating boundary (which is planar for equal volumes) separate two volumes of air with less Area than any other boundary. The planar case was proved true for equal volumes by J. Hass and R. Schlafy in 1995 by reducing the problem to a set of 200,260 integrals which they carried out on an ordinary PC.
See also Double Bubble
References
Haas, J.; Hutchings, M.; and Schlafy, R. ``The Double Bubble Conjecture.'' Electron. Res. Announc. Amer. Math. Soc.
1, 98-102, 1995.