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Creators/Authors contains: "Bongiovanni, Eliot"

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  1. ; ; ; (, Missouri journal of mathematical sciences)
    The isoperimetric problem with a density or weighting seeks to enclose prescribed weighted volume with minimum weighted perimeter. According to Chambers' recent proof of the log-convex density conjecture, for many densities on Rn the answer is a sphere about the origin. We seek to generalize his results to some other spaces of revolution or to two di erent densities for volume and perimeter. We provide general results on existence and boundedness and a new approach to proving circles about the origin isoperimetric. 
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    Accepted Manuscript Full Text Available
  2. ; ; ; ; ; ; ; ; (, Analysis and Geometry in Metric Spaces)
    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). 
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