Document Type
Lecture
Publication Date
9-10-2010
Abstract
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. Specifically, 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. Applications of this result to external field problems and constrained energy problems will be discussed.
Relational Format
presentation
Recommended Citation
Dragnev, Peter, "Ping pong balayage and convexity of the Riesz and logarithmic equilibrium measures" (2010). Analysis Seminar. 20.
https://egrove.olemiss.edu/math_analysis/20
