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arXiv · 0811.3413

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

Joseph Corneli·Neil Hoffman·Paul Holt·George Lee·Nicholas Leger·Stephen Moseley·Eric Schoenfeld
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Abstract

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

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Joseph Corneli, Neil Hoffman, Paul Holt, George Lee, Nicholas Leger, Stephen Moseley, Eric Schoenfeld. 2008-12-11. Double bubbles in $S^3$ and $H^3$. https://arxiv.org/abs/0811.3413

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