10th Summer School in Potential Theory
Minimal energy problems in the presence of external fields are a classic topic in logarithmic potential theory in the complex plane. Applications vary from asymptotics of orthogonal polynomials, to fast decreasing polynomials, to weighted polynomial and rational approximation, etc. Here we shall introduce the counterpart for measures supported on the unit sphere, with motivation arising from an application to separation results for minimal Riesz s-energy spherical configurations. A natural extension to axis-symmetric external fields is presented and separation results for minimal energy points with external fields. Finally, a work in progress report considers the special case s=d-2, where the external field is explicitly solved for discrete Riesz potential with mass points on the sphere and small enough charges at the mass points.
Riesz potential, minimal energy, external fields
Analysis | Numerical Analysis and Computation | Other Physical Sciences and Mathematics
Peter D. Dragnev, Peter Boyvalenkov, Douglas P. Hardin, Edward Saff, and Maya Stoyanova (2015).
External field energy problems on the sphere and minimal energy points separation. Presented at 10th Summer School in Potential Theory, Budapest, Hungary.