The structure of area-minimizing double bubbles
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We show that the least area required to enclose two volumes in ℝn orSn forn ≥ 3 is a strictly concave function of the two volumes. We deduce that minimal double bubbles in ℝn have no empty chambers, and we show that the enclosed regions are connected in some cases. We give consequences for the structure of minimal double bubbles in ℝn. We also prove a general symmetry theorem for minimal enclosures ofm volumes in ℝn, based on an idea due to Brian White.
Math Subject Classification53C20
Key Words and PhrasesSoap bubbles isoperimetric problems
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