Isoperimetric Regions in ${\mathbb{R}}^n$ with density $r^p$

Abstract

We show that the unique isoperimetric hypersurfaces in ${\mathbb{R}}^n$ with density $r^p$ for $n\ge 3$ and $p>0$ are spheres that pass through the origin.

published online in Analysis and Geometry in Metric Spaces, revised according to referee report, 29 pages, 10 figures

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