Abstract
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 language | English (US) |
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Pages (from-to) | 51-86 |
Number of pages | 36 |
Journal | Pure and Applied Mathematics Quarterly |
Volume | 7 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2011 |
Keywords
- Capacity
- Critical points
- Equilibrium potential
- Extremal problem
- Green's function
- Polynomials
- Zeros
ASJC Scopus subject areas
- General Mathematics