English

Double bubbles in $S^3$ and $H^3$

Differential Geometry 2008-12-12 v2

Abstract

We prove the double bubble conjecture in the three-sphere S3S^3 and hyperbolic three-space H3H^3 in the cases where we can apply Hutchings theory: 1) in S3S^3, each enclosed volume and the complement occupy at least 10% of the volume of S3S^3; 2) in H3H^3, the smaller volume is at least 85% that of the larger. A balancing argument and asymptotic analysis reduce the problem in S3S^3 and H3H^3 to some computer checking. The computer analysis has been designed and fully implemented for both spaces.

Keywords

Cite

@article{arxiv.0811.3413,
  title  = {Double bubbles in $S^3$ and $H^3$},
  author = {Joseph Corneli and Neil Hoffman and Paul Holt and George Lee and Nicholas Leger and Stephen Moseley and Eric Schoenfeld},
  journal= {arXiv preprint arXiv:0811.3413},
  year   = {2008}
}

Comments

Version 1:52 pages (including 18 pages of unpublished computer code), 10 figures Version 2: Improved quality on all 10 figures

R2 v1 2026-06-21T11:43:48.613Z