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arXiv · 1012.0450

Isoperimetric problems in sectors with density

Alexander Díaz·Nate Harman·Sean Howe·David Thompson
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Abstract

We consider the isoperimetric problem in planar sectors with density $r^{p}$, and with density $a>1$ inside the unit disk and $1$ outside. We characterize solutions as a function of sector angle. We also solve the isoperimetric problem in $\mathbb{R}^{n}$ with density $r^{p},\; p<0$.

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Alexander Díaz, Nate Harman, Sean Howe, David Thompson. 2010-12-02. Isoperimetric problems in sectors with density. https://arxiv.org/abs/1012.0450

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