An isoperimetric inequality in the plane with a log-convex density

I. McGillivray*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)
285 Downloads (Pure)


Given a positive lower semi-continuous density f on (Formula presented.) the weighted volume (Formula presented.) is defined on the (Formula presented.)-measurable sets in (Formula presented.). The f-weighted perimeter of a set of finite perimeter E in (Formula presented.) is written (Formula presented.). We study minimisers for the weighted isoperimetric problem (Formula presented.)for (Formula presented.). Suppose f takes the form (Formula presented.) where (Formula presented.) is a non-decreasing convex function. Let (Formula presented.) and B a centred ball in (Formula presented.) with (Formula presented.). We show that B is a minimiser for the above variational problem and obtain a uniqueness result.

Original languageEnglish
Pages (from-to)1-58
Number of pages58
JournalRicerche di Matematica
Early online date21 Mar 2018
Publication statusE-pub ahead of print - 21 Mar 2018


  • Generalised mean curvature
  • Isoperimetric problem
  • Log-convex density


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