Moment inequalities for equilibrium measures in the plane

Details Moment inequalities for equilibrium measures in the plane Moment inequalities for equilibrium measures in the plane

2007-02-15

arxiv.org/abs/math/0702456v1

Mathematics

Complex Variables

28 pages

Scientific paper

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.

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