Geodesic
The double bubble conjecture
Hass, Joel1 ; Hutchings, Michael2 ; Schlafly, Roger3
1 Department of Mathematics, University of California, Davis, CA 95616
2 Department of Mathematics, Harvard University, Cambridge, MA 02138
3 Real Software, PO Box 1680, Soquel, CA 95073
Electronic research announcements of the American Mathematical Society, Tome 01 (1995) no. 3, pp. 98-102.

Voir la notice de l'article provenant de la source American Mathematical Society

The classical isoperimetric inequality states that the surface of smallest area enclosing a given volume in $R^3$ is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of $2 \pi / 3$.
DOI : 10.1090/S1079-6762-95-03001-0

Hass, Joel 1 ; Hutchings, Michael 2 ; Schlafly, Roger 3

1 Department of Mathematics, University of California, Davis, CA 95616
2 Department of Mathematics, Harvard University, Cambridge, MA 02138
3 Real Software, PO Box 1680, Soquel, CA 95073 
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Hass, Joel; Hutchings, Michael; Schlafly, Roger. The double bubble conjecture. Electronic research announcements of the American Mathematical Society, Tome 01 (1995) no. 3, pp. 98-102. doi : 10.1090/S1079-6762-95-03001-0. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-95-03001-0/

[1] Foisy, Joel, Alfaro, Manuel, Brock, Jeffrey, Hodges, Nickelous, Zimba, Jason The standard double soap bubble in 𝑅² uniquely minimizes perimeter Pacific J. Math. 1993 47 59

[2] Almgren, F. J., Jr. Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints Mem. Amer. Math. Soc. 1976

[3] Eells, James The surfaces of Delaunay Math. Intelligencer 1987 53 57

[4] Morgan, Frank Clusters minimizing area plus length of singular curves Math. Ann. 1994 697 714

[5] Moore, Ramon E. Methods and applications of interval analysis 1979

[6] Taylor, Jean E. The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces Ann. of Math. (2) 1976 489 539

[7] Thompson, D’Arcy Wentworth On growth and form 1961

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