Double bubbles inS 3 andH 3

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

Research output: Contribution to journalArticlepeer-review

6 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 languageEnglish (US)
Pages (from-to)189-212
Number of pages24
JournalJournal of Geometric Analysis
Volume17
Issue number2
DOIs
StatePublished - 2007
Externally publishedYes

Keywords

  • Double bubbles

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