Uniform Green packing on compact Riemann surfaces

Abstract

We extend the packing results of Etayo, Hedenmalm, and Ortega-Cerda for complex tori to arbitrary compact Riemann surfaces. The construction uses two different approaches, one based on complex geometry of line bundles, and the other on Laplace designs. Both approaches give the same basic existence of close-to-optimal point configurations on the given surface. This version was written with the help of ChatGPT.