The droplet generated by two point charges on a sphere

by Juan Criado del Rey (KU Leuven)

Location: 200B.02.18, Leuven
Time: Wednesday April 17, 2019 at 10:30

Consider the external field on the two dimensional sphere generated by two point charges by means of the logarithmic potential. It follows from the general theory that the minimizing probability measure for the corresponding weighted energy problem is supported on a set D (the droplet) and has constant density on D. Previous works by Brauchart, Dragnev, Saff and Womersley show that if the charges are small, then D is the complement of two spherical caps. In this talk we will see what the shape of D is when the two charges are equal but arbitrarily large.

This is joint work with Alan Groot and Arno Kuijlaars.