Hass, Joel; Hutchings, Michael; Schlafly, Roger The double bubble conjecture. (English) Zbl 0864.53007 Electron. Res. Announc. Am. Math. Soc. 1, No. 3, 98-102 (1995). The authors prove 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 \(2\pi/3\).The proof builds upon techniques mainly due to F. Almgren and J. Taylor as well as those of B. White and F. Morgan. The ideas are discussed in a clear manner. Reviewer: Th.M.Rassias (Athens) Cited in 17 Documents MSC: 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 49Q10 Optimization of shapes other than minimal surfaces 49Q20 Variational problems in a geometric measure-theoretic setting Keywords:double bubble conjecture; isoperimetric inequality; numerical integration; least area surface × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Joel Foisy, Manuel Alfaro, Jeffrey Brock, Nickelous Hodges, and Jason Zimba, The standard double soap bubble in \?² uniquely minimizes perimeter, Pacific J. Math. 159 (1993), no. 1, 47 – 59. · Zbl 0738.49023 [2] F. J. Almgren Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, Mem. Amer. Math. Soc. 4 (1976), no. 165, viii+199. · Zbl 0327.49043 · doi:10.1090/memo/0165 [3] F.J. Almgren and J. Taylor, The geometry of soap films and soap bubbles, Sci. Amer. 235,82-93 (1976). [4] ANSI/IEEE Standard 754-1985 for Binary Floating-Point Arithmetic, The Institute of Electrical and Electronic Engineers, New York, 1985. [5] C.V. Boys, Soap Bubbles, Dover Publ. Inc. NY 1959 (first edition 1911). [6] C. Delaunay, Sur la surface de revolution dont la courbure moyenne est constante, J. Math. Pure et App. 16, 309-321 (1841). [7] James Eells, The surfaces of Delaunay, Math. Intelligencer 9 (1987), no. 1, 53 – 57. · Zbl 0605.53002 · doi:10.1007/BF03023575 [8] J. Foisy, Soap bubble clusters in \(R^2\) and \(R^3\), undergraduate thesis, Williams College (1991). [9] J. Hass and R. Schlafly, Double Bubbles Minimize, (preprint). · Zbl 0970.53008 [10] M. Hutchings, The structure of area-minimizing double bubbles, to appear in J. Geom. Anal. · Zbl 0935.53008 [11] Frank Morgan, Clusters minimizing area plus length of singular curves, Math. Ann. 299 (1994), no. 4, 697 – 714. · Zbl 0805.49025 · doi:10.1007/BF01459806 [12] Ramon E. Moore, Methods and applications of interval analysis, SIAM Studies in Applied Mathematics, vol. 2, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa., 1979. · Zbl 0417.65022 [13] J. Plateau, Statique expérimentale et théorique des liquides soumis aux seules forces moleculaires, Gathier-Villars, Paris, 1873. · JFM 06.0516.03 [14] Jean E. Taylor, The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces, Ann. of Math. (2) 103 (1976), no. 3, 489 – 539. , https://doi.org/10.2307/1970949 Jean E. Taylor, The structure of singularities in solutions to ellipsoidal variational problems with constraints in \?³, Ann. of Math. (2) 103 (1976), no. 3, 541 – 546. · Zbl 0335.49033 · doi:10.2307/1970950 [15] D’Arcy Wentworth Thompson, On growth and form, An abridged edition edited by John Tyler Bonner, Cambridge University Press, New York, 1961. · Zbl 0063.07372 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.