The Journal of Geometric Analysis

, Volume 7, Issue 2, pp 285–304

The structure of area-minimizing double bubbles

  • Michael Hutchings


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 Classification


Key Words and Phrases

Soap bubbles isoperimetric problems 


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Copyright information

© Mathematica Josephina, Inc. 1997

Authors and Affiliations

  • Michael Hutchings
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridge

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