Moment inequalities for equilibrium measures in the plane

A. Baernstein, R. S. Laugesen, I. E. Pritske

Research output: Contribution to journalArticlepeer-review


The equilibrium measure of a compact plane set gives the steady state distribution of charges on the conductor. We show that certain moments of this equilibrium measure, when taken about the electrostatic centroid and depending only on the real coordinate, are extremal for an interval centered at the origin. This has consequences for means of zeros of polynomials, and for means of critical points of Green's functions. We also study moments depending on the distance from the centroid, such as the electrostatic moment of inertia.

Original languageEnglish (US)
Pages (from-to)51-86
Number of pages36
JournalPure and Applied Mathematics Quarterly
Issue number1
StatePublished - Jan 2011


  • Capacity
  • Critical points
  • Equilibrium potential
  • Extremal problem
  • Green's function
  • Polynomials
  • Zeros

ASJC Scopus subject areas

  • General Mathematics


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