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

Alyssa Loving; Bryan Brown; Gregory R. Chambers; Sarah Tammen; Wyatt Boyer

arxiv: 1504.01720 · v3 · pith:FEANYRCInew · submitted 2015-04-07 · 🧮 math.DG

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

Wyatt Boyer , Bryan Brown , Gregory R. Chambers , Alyssa Loving , Sarah Tammen This is my paper

classification 🧮 math.DG

keywords densityisoperimetricmathbbhypersurfacesoriginpassregionsspheres

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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.

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

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