Proof of the Double Bubble Conjecture

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Michael Hutchings , Frank Morgan , Manuel Ritoré , Antonio Ros This is my paper · ORCID

classification math.DGmath.MG

keywords bubbledoubleconjectureencloseleast-areaprescribedproofprove

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We prove that the standard double bubble provides the least-area way to enclose and separate two regions of prescribed volume in \Bbb R^3.

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The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$
math.AP 2026-04 unverdicted novelty 7.0 of 10

For regular anisotropies the unique local minimizers of the anisotropic perimeter for (1,2) and (1,3) clusters in R^2 are the anisotropic lens and triod clusters respectively.