Proof of the Double Bubble Conjecture

American Mathematical Monthly

Volumn 108, Issue 3, 2001, Pages 193-205

  Morgan, Frank ^a  

^a WILLIAMS COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035584526     PISSN: 00029890     EISSN: None     Source Type: Journal    
DOI: 10.2307/2695380     Document Type: Article

References (16)

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2. 2, Real Anal. Exchange 20 (1994/95) 313-335.
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4. Barry Cipra, Why double bubbles form the way they do, Science 287 ( 17 March 2000) 1910-1911.
5. 3, undergraduate thesis, Williams College, 1991.
6. 2 uniquely minimizes perimeter, Pacific J. Math. 159 (1993) 47-59.
7. Joel Hass, Michael Hutchings, and Roger Schlafly, The double bubble conjecture, Electron. Res. Announc. Amer. Math. Soc. 1 (1995) 98-102.
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9. Joel Hass and Roger Schlafly, Double bubbles minimize, Ann. Math. 151 (2000) 459-515.
10. Cory Heilmann, Yuan Y. Lai, Ben W. Reichardt, and Anita Spielman, Component bounds for area-minimizing double bubbles, NSF "SMALL" undergraduate research Geometry Group report, Williams College, 1999.
11. Michael Hutchings, Frank Morgan, Manuel Ritoré, and Antonio Ros, Proof of the double bubble conjecture, Electron. Res. Announc. Amer. Math. Soc. 6 (2000) 45-49. Preprint of full paper at www.ugr.es/-ritore/bubble/bubble.htm.
12. Michael Hutchings, The structure of area-minimizing double bubbles, J. Geom. Anal. 7 (1997) 285-304.
13. Frank Morgan, Geometric Measure Theory: a Beginner's Guide, third ed., Academic Press, Boston, 2000.
14. J. Plateau, Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires, Paris, Gauthier-Villars, 1873.
15. 4 and certain higher dimensions, Pacific J. Math., to appear.
16. John M. Sullivan and Frank Morgan, ed., Open problems in soap bubble geometry, Internat. J. Math. 7 (1996) 833-842.