Open Access
June 15, 2018
### Abstract

The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in ℝ N is the standard double bubble. We seek the optimal double bubble in ℝ N 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).