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Zbl 1003.53010
Morgan, Frank; Wichiramala, Wacharin
The standard double bubble is the unique stable double bubble in $\bbfR^2$. (English)
[J] Proc. Am. Math. Soc. 130, No.9, 2745-2751 (2002). ISSN 0002-9939; ISSN 1088-6826/e

{\it J.~Foisy, M.~Alfaro, J.~Brock, N.~Hodges}, and {\it J.~Zimba} [Pac. J. Math. 159, No. 1, 47-59 (1993; Zbl 0738.49023)] proved that the standard double bubble consisting of three constant-curvature arcs meeting at 120 degrees is the unique least-perimeter way to enclose and separate two planar regions of prescribed areas. The regions are not assumed to be connected. The proof left open the question of whether there might be other stable double bubbles. In this paper, the authors prove that the only equilibrium double bubble in $\Bbb {R}^2$ which is stable for fixed areas is the standard double bubble. This uniqueness result also holds for small stable double bubbles in surfaces, where it is new even for perimeter-minimizing double bubbles.
[Andrew Bucki (Oklahoma City)]

MSC 2000:: *53A10 Minimal surfaces, surfaces with prescribed mean curvature
49Q20 Variational problems in geometric measure-theoretic setting

Keywords: stable double bubble; standard double bubble; soap bubble

Citations: Zbl 0738.49023

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