Minimizing capacity among linear images of rotationally invariant conductors

Research output: Contribution to journalArticlepeer-review


Logarithmic capacity is shown to be minimal for a planar set having N-fold rotational symmetry (N≥ 3), among all conductors obtained from the set by area-preserving linear transformations. Newtonian and Riesz capacities obey a similar property in all dimensions, when suitably normalized linear transformations are applied to a set having irreducible symmetry group. A corollary is Pólya and Schiffer’s lower bound on capacity in terms of moment of inertia.

Original languageEnglish (US)
Article number21
JournalAnalysis and Mathematical Physics
Issue number1
StatePublished - Feb 2022


  • Isoperimetric
  • Riesz kernel
  • Shape optimization

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics


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