Geodesic
Proof of the double bubble conjecture
Hutchings, Michael1 ; Morgan, Frank2 ; Ritoré, Manuel3 ; Ros, Antonio3
1 Department of Mathematics, Stanford University, Stanford, CA 94305
2 Department of Mathematics, Williams College, Williamstown, MA 01267
3 Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, España
Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 45-49 Cet article a éte moissonné depuis la source American Mathematical Society

Voir la notice de l'article

We prove that the standard double bubble provides the least-area way to enclose and separate two regions of prescribed volume in ${\mathbb R}^3$.
DOI : 10.1090/S1079-6762-00-00079-2

Hutchings, Michael 1 ; Morgan, Frank 2 ; Ritoré, Manuel 3 ; Ros, Antonio 3

1 Department of Mathematics, Stanford University, Stanford, CA 94305
2 Department of Mathematics, Williams College, Williamstown, MA 01267
3 Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, España 
@article{10_1090_S1079_6762_00_00079_2,
     author = {Hutchings, Michael and Morgan, Frank and Ritor\'e, Manuel and Ros, Antonio},
     title = {Proof of the double bubble conjecture},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {45--49},
     year = {2000},
     volume = {06},
     doi = {10.1090/S1079-6762-00-00079-2},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-00-00079-2/}
}
TY  - JOUR
AU  - Hutchings, Michael
AU  - Morgan, Frank
AU  - Ritoré, Manuel
AU  - Ros, Antonio
TI  - Proof of the double bubble conjecture
JO  - Electronic research announcements of the American Mathematical Society
PY  - 2000
SP  - 45
EP  - 49
VL  - 06
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-00-00079-2/
DO  - 10.1090/S1079-6762-00-00079-2
ID  - 10_1090_S1079_6762_00_00079_2
ER  - 
%0 Journal Article
%A Hutchings, Michael
%A Morgan, Frank
%A Ritoré, Manuel
%A Ros, Antonio
%T Proof of the double bubble conjecture
%J Electronic research announcements of the American Mathematical Society
%D 2000
%P 45-49
%V 06
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-00-00079-2/
%R 10.1090/S1079-6762-00-00079-2
%F 10_1090_S1079_6762_00_00079_2
Hutchings, Michael; Morgan, Frank; Ritoré, Manuel; Ros, Antonio. Proof of the double bubble conjecture. Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 45-49. doi: 10.1090/S1079-6762-00-00079-2

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

[2] Nakayama, Tadasi On Frobeniusean algebras. I Ann. of Math. (2) 1939 611 633

[3] 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

[4] Hass, Joel, Hutchings, Michael, Schlafly, Roger The double bubble conjecture Electron. Res. Announc. Amer. Math. Soc. 1995 98 102

[5] Hutchings, Michael The structure of area-minimizing double bubbles J. Geom. Anal. 1997 285 304

[6] Knorr, Wilbur Richard The ancient tradition of geometric problems 1986

[7] Morgan, Frank Geometric measure theory 1995

[8] Ritoré, Manuel, Ros, Antonio Stable constant mean curvature tori and the isoperimetric problem in three space forms Comment. Math. Helv. 1992 293 305

[9] Ros, Antonio, Souam, Rabah On stability of capillary surfaces in a ball Pacific J. Math. 1997 345 361

[10] Ros, Antonio, Vergasta, Enaldo Stability for hypersurfaces of constant mean curvature with free boundary Geom. Dedicata 1995 19 33

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

Cité par Sources :