Proof of the double bubble conjecture

We prove that the standard double bubble provides the least-area way to enclose and separate two regions of prescribed volume in R3.Morgan has partial support from a National Science Foundation grant. Ritoré and Ros have partial support from DGICYT research group n. PB97-0785

The double bubble conjecture

Abstract. The classical isoperimetric inequality states that the surface of smallest area enclosing a given volume in R 3 is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 2π/3. 1