### Abstract

We consider the isoperimetric problem in the plane with density r^{p}, p > 0, and prove that the solution is a circle through the origin. We use the stability of this isoperimetric curve to prove an apparently new generalization of Wirtinger's Inequality.

Original language | English |
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Pages (from-to) | 31-51 |

Number of pages | 21 |

Journal | New York Journal of Mathematics |

Volume | 16 |

State | Published - 2010 |

### Keywords

- Isoperimetric
- Plane with density
- Radial densities
- Symmetrization

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## Cite this

Dahlberg, J., Dubbs, A., Newkirk, E., & Tran, H. (2010). Isoperimetric regions in the plane with density r

^{p}.*New York Journal of Mathematics*,*16*, 31-51.