The Journal of Geometric Analysis

, Volume 17, Issue 2, pp 189–212

Double bubbles inS3 andH3

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

DOI: 10.1007/BF02930720

Cite this article as:
Corneli, J., Hoffman, N., Holt, P. et al. J Geom Anal (2007) 17: 189. doi:10.1007/BF02930720

Abstract

We prove the double bubble conjecture in the three-sphereS3 and hyperbolic three-spaceH3 in the cases where we can apply Hutchings theory:
  • • InS3, when each enclosed volume and the complement occupy at least 10% of the volume ofS3.

  • • inH3, when the smaller volume is at least 85% that of the larger.

A balancing argument and asymptotic analysis reduce the problem inS3 andH3 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 

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