Ping Pong Balayage and Convexity of Equilibrium Measures
University of Mississippi Analysis Seminar
Oxford, MS, USA
In this presentation I will prove that the equilibrium measure of a compact subset on the real line or unit circle has essentially convex density, namely if the compact set contains an interval, its equilibrium measure is absolutely continuous and has a convex density. This is true for both, the classical logarithmic case, and the Riesz case.
The electrostatic interpretation is the following: if we have a finite union of subintervals on the real line, or arcs on the unit circle, the electrostatic distribution of many ”electrons” will have convex density on every subinterval.
I will present applications of this result to external field problems and constrained energy problems. I will try to keep jargon at minimal, so the presentation is accessible to a broader audience.
Analysis | Mathematics
Peter D. Dragnev (2010).
Ping Pong Balayage and Convexity of Equilibrium Measures. Presented at University of Mississippi Analysis Seminar, Oxford, MS, USA.