Minimal Energy Problems and Applications: Ping Pong Balayage and Convexity of Equilibrium Measures

Document Type


Presentation Date


Conference Name

University of South Alabama Colloquium

Conference Location

Mobile, AL, USA

Peer Review



This talk has two parts. Initially, I will present a survey of various minimal energy problems in potential theory having applications to different areas of research not only in mathematics, but in physics, biology, chemistry, etc. In addition to being a preview of a sequence of more detailed lectures to be given at subsequent colloquia and analysis seminars, the survey will introduce the necessary preliminaries to present the main result.

Let E be the union of finitely many intervals or arcs on the unit circle. In a joint work with David Benko we prove that the equilibrium measure of E has a convex density. This is true for both the classical logarithmic kernel, and the Riesz kernel. This seems to be a fundamental result in potential theory, maybe one for the books.

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.


Analysis | Mathematics

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