Min-Max Polarization for Certain Classes of Sharp Configurations on the Sphere

Sergiy Borodachov (Towson U)

Jan 17. 2022, 14:00 — 14:40

We consider the problem of finding N-point configurations on a d-dimensional Euclidean sphere with the smallest absolute maximum value of their total potential over the sphere. The kernel is the value of a given potential function f at the Euclidean distance squared,  where f is continuous on [0,4] and completely monotone on (0,4] modulo an additive constant. We show that any sharp configuration, which is antipodal or is a spherical design of an even strength is a solution to this problem. We also prove that the absolute maximum over the sphere of the potential of any such configuration is attained at points of that configuration. 

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Optimal Point Configurations on Manifolds (Workshop)
Christine Bachoc (U Bordeaux)
Henry Cohn (Microsoft, Redmond)
Peter Grabner (TU Graz)
Douglas Hardin (Vanderbilt U, Nashville)
Edward Saff (Vanderbilt U, Nashville)
Achill Schürmann (U of Rostock)
Robert Womersley (UNSW, Sydney)