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The double bubble conjecture. (English) Zbl 0864.53007

The authors prove 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 \(2\pi/3\).
The proof builds upon techniques mainly due to F. Almgren and J. Taylor as well as those of B. White and F. Morgan. The ideas are discussed in a clear manner.

MSC:

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
49Q10 Optimization of shapes other than minimal surfaces
49Q20 Variational problems in a geometric measure-theoretic setting
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References:

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