Isoperimetric regions in the plane with density rp

Jonathan Dahlberg, Alexander Dubbs, Edward Newkirk, Hung Tran

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


We consider the isoperimetric problem in the plane with density rp, 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 languageEnglish
Pages (from-to)31-51
Number of pages21
JournalNew York Journal of Mathematics
StatePublished - 2010


  • Isoperimetric
  • Plane with density
  • Radial densities
  • Symmetrization


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