Abstract The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in ℝN is the standard double bubble. We seek the optimal double bubble in ℝN with density, which we assume to be strictly log-convex. For N = 1 we show that the solution is sometimes two contiguous intervals and sometimes three contiguous intervals. In higher dimensions we think that the solution is sometimes a standard double bubble and sometimes concentric spheres (e.g. for one volume small and the other large).

中文翻译：

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具有对数凸密度的实线上的双气泡

摘要 经典的双气泡定理说，在ℝN 中包围和分离两个指定体积的最小周长方法是标准双气泡。我们在 ℝN 中寻找具有密度的最优双气泡，我们假设它是严格对数凸的。对于 N = 1，我们表明解有时是两个连续的区间，有时是三个连续的区间。在更高的维度中，我们认为解决方案有时是标准的双气泡，有时是同心球（例如，一个体积小，另一个体积大）。