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- W2000895919 abstract "An area minimizing double bubble in ℝn is given by two (not necessarily connected) regions which have two prescribed n-dimensional volumes whose combined boundary has least (n−1)-dimensional area. The double bubble theorem states that such an area minimizer is necessarily given by a standard double bubble, composed of three spherical caps. This has now been proven for n = 2, 3,4, but is, for general volumes, unknown for n ≥ 5. Here, for arbitrary n, we prove a conjectured lower bound on the mean curvature of a standard double bubble. This provides an alternative line of reasoning for part of the proof of the double bubble theorem in ℝ3, as well as some new component bounds in ℝn." @default.
- W2000895919 created "2016-06-24" @default.
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- W2000895919 date "2007-03-01" @default.
- W2000895919 modified "2023-09-26" @default.
- W2000895919 title "Proof of the double bubble curvature conjecture" @default.
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- W2000895919 doi "https://doi.org/10.1007/bf02922083" @default.
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