Proof of the double bubble conjecture in R4 and certain higher dimensional cases

Pacific Journal of Mathematics

Volumn 208, Issue 2, 2003, Pages 347-366

  Reichardt, Ben W ^a   Heilmann, Cory ^d   Lai, Yuan Y ^b   Spielman, Anita ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c WILLIAMS COLLEGE   (United States)

^d NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037310461     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.2003.208.347     Document Type: Article

References (11)

1. [A] F.J. Almgren, Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems with, constraints, Memoirs Amer. Math. Soc., 165(4) (1976), 1-199, MR 54 #8420, Zbl 0327.49043.
2. [D] C. Delaunay, Sur la surface de révolution dont la courbure moyenne est constante, J. Math. Pures. Appl. Sér 1, 6 (1841), 309-320.
3. [E] J. Eells, The surfaces of Delaunay, Math. Intelligencer, 9 (1987), 53-57, MR. 88h:53011, Zbl 0605.53002.
4. 2 uniquely minimizes perimeter, Pacific J. Math., 159 (1993), 47-59, MR 94b:53019, Zbl 0738.49023.
5. [HHS] J. Hass, M. Hutchings and R. Schlafly, The double bubble conjecture, Elec. Res. Ann. Amer. Math. Soc., 1 (1995), 98-102, MR 97b:53014, Zbl 0864.53007.
6. [HS] J. Haas and R. Schlafly, Double bubbles minimize, Ann. Math., 151 (2000), 459-515, MR 2002d:53018, Zbl 0970.53008.
7. [HLRS] C. Heilmann, Y. Lai, B. Reichardt and A. Spielman, Component bounds for area-minimizing double bubbles, NSF "SMALL" undergraduate research Geometry Group report, Williams College, 1999.
8. [HY] W.-Y. Hsiang and W.-C. Yu, A generalization of a theorem of Delaunay, J. Differential Geom., 16 (1981), 161-177, MR 83f:53001, Zbl 0504.53044.
9. [H] M. Hutchings, The structure of area-minimizing double bubbles, J. Geom. Anal., 7 (1997), 285-304, MR 99j:53010, Zbl 0935.53008.
10. [HMRH] M. Hutchings, F. Morgan, M. Ritoré and A. Ros, Proof of the double bubble conjecture. Preprint, 2000; Research announcement, Electron. Res. Announc. Amer, Math. Soc., 6 (2000), 45-49, MR 2001m:53011, Zbl 0970.53009.
11. [M] F. Morgan, Geometric Measure Theory: A Beginner's Guide, Academic Press, 3rd ed., 2000, MR, 2001j:49001, Zbl 0974.49025.