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 and hyperbolic three-space in the cases where we can apply Hutchings theory: 1) in , each enclosed volume and the complement occupy at least 10% of the volume of ; 2) in , the smaller volume is at least 85% that of the larger. A balancing argument and asymptotic analysis reduce the problem in and to some computer checking. The computer analysis has been designed and fully implemented for both spaces.
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Version 1:52 pages (including 18 pages of unpublished computer code), 10 figures Version 2: Improved quality on all 10 figures