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The Journal of Geometric Analysis

, Volume 17, Issue 2, pp 189–212 | Cite as

Double bubbles inS 3 andH 3

  • Joseph Corneli
  • Neil Hoffman
  • Paul Holt
  • George Lee
  • Nicholas Leger
  • Stephen Moseley
  • Eric Schoenfeld
Article

Abstract

We prove the double bubble conjecture in the three-sphereS 3 and hyperbolic three-spaceH 3 in the cases where we can apply Hutchings theory:
  • • InS 3, when each enclosed volume and the complement occupy at least 10% of the volume ofS 3.

  • • inH 3, when the smaller volume is at least 85% that of the larger.

A balancing argument and asymptotic analysis reduce the problem inS 3 andH 3 to some computer checking. The computer analysis has been designed and fully implemented for both spaces.

Math Subject Classifications

53C42 

Key Words and Phrases

Double bubbles 

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Copyright information

© Mathematica Josephina, Inc. 2007

Authors and Affiliations

  • Joseph Corneli
    • 1
  • Neil Hoffman
    • 1
  • Paul Holt
    • 2
  • George Lee
    • 2
  • Nicholas Leger
    • 1
  • Stephen Moseley
    • 3
  • Eric Schoenfeld
    • 4
  1. 1.Department of MathematicsUniversity of TexasAustin
  2. 2.Department of Mathematics and StatisticsWilliams CollegeWilliamstown
  3. 3.Center for Applied MathematicsCornell UniversityIthaca
  4. 4.Stanford University, MathematicsStanford

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