Double bubbles in S³ and H³

الأصل · EN

We prove the double bubble conjecture in the three-sphere S³ and hyperbolic three-space H³ in the cases where we can apply Hutchings theory: 1) in S³, each enclosed volume and the complement occupy at least 10% of the volume of S³; 2) in H³, the smaller volume is at least 85% that of the larger. A balancing argument and asymptotic analysis reduce the problem in S³ and H³ to some computer checking. The computer analysis has been designed and fully implemented for both spaces.