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

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

doi:10.1515/agms-2016-0009

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arXiv · 1504.01720

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

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

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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.

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BibTeX RIS

Wyatt Boyer, Bryan Brown, Gregory R. Chambers, Alyssa Loving, Sarah Tammen. 2015-04-07. Isoperimetric Regions in $\mathbb{R}^n$ with density $r^p$. https://doi.org/10.1515/agms-2016-0009

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