Double bubbles inS 3 andH 3

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

doi:10.1007/BF02930720

Double bubbles inS ³ andH ³

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

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We prove the double bubble conjecture in the three-sphereS ³ and hyperbolic three-spaceH ³ in the cases where we can apply Hutchings theory: • InS ³, when each enclosed volume and the complement occupy at least 10% of the volume ofS ³. • inH ³, when the smaller volume is at least 85% that of the larger. A balancing argument and asymptotic analysis reduce the problem inS ³ andH ³ to some computer checking. The computer analysis has been designed and fully implemented for both spaces.

Original language	English (US)
Pages (from-to)	189-212
Number of pages	24
Journal	Journal of Geometric Analysis
Volume	17
Issue number	2
DOIs	https://doi.org/10.1007/BF02930720
State	Published - 2007
Externally published	Yes

Keywords

Double bubbles

Publisher link

10.1007/BF02930720

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Cite this

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title = "Double bubbles inS 3 andH 3 ",

abstract = "We prove the double bubble conjecture in the three-sphereS 3 and hyperbolic three-spaceH 3 in the cases where we can apply Hutchings theory: • InS 3, when each enclosed volume and the complement occupy at least 10\% of the volume ofS 3. • inH 3, when the smaller volume is at least 85\% that of the larger. A balancing argument and asymptotic analysis reduce the problem inS 3 andH 3 to some computer checking. The computer analysis has been designed and fully implemented for both spaces.",

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AU - Corneli, Joseph

AU - Hoffman, Neil

AU - Holt, Paul

AU - Lee, George

AU - Leger, Nicholas

AU - Moseley, Stephen

AU - Schoenfeld, Eric

PY - 2007

Y1 - 2007

N2 - We prove the double bubble conjecture in the three-sphereS 3 and hyperbolic three-spaceH 3 in the cases where we can apply Hutchings theory: • InS 3, when each enclosed volume and the complement occupy at least 10% of the volume ofS 3. • inH 3, when the smaller volume is at least 85% that of the larger. A balancing argument and asymptotic analysis reduce the problem inS 3 andH 3 to some computer checking. The computer analysis has been designed and fully implemented for both spaces.

AB - We prove the double bubble conjecture in the three-sphereS 3 and hyperbolic three-spaceH 3 in the cases where we can apply Hutchings theory: • InS 3, when each enclosed volume and the complement occupy at least 10% of the volume ofS 3. • inH 3, when the smaller volume is at least 85% that of the larger. A balancing argument and asymptotic analysis reduce the problem inS 3 andH 3 to some computer checking. The computer analysis has been designed and fully implemented for both spaces.

KW - Double bubbles

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UR - https://www.scopus.com/pages/publications/84867965027#tab=citedBy

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JF - Journal of Geometric Analysis

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