Ping Pong Balayage and Convexity of Equilibrium Measures
University of North Florida Colloquium
Jacksonville, FL, USA
In this joint work with David Benko from the University of South Alabama we prove that the equilibrium measure of a finite union of intervals on the real line or arcs on the circle is absolutely continuous and has a convex density, a fundamental result in Potential theory, may be one for the books. This is true for both, the classical logarithmic case, and the Riesz case.
The Physics interpretation would be that the electrostatic distribution of many "electrons" on finitely many intervals/arcs has convex density. Applications of this result to external field problems and constrained energy problems are given.
Analysis | Mathematics
Peter D. Dragnev and Benko David (2010).
Ping Pong Balayage and Convexity of Equilibrium Measures. Presented at University of North Florida Colloquium, Jacksonville, FL, USA.