Energy Minimization Principle for non-archimedean curves

Abstract

Baker and Rumely defined a notion of Arakelov-Green's functions on the Berkovich analytification of the projective line and established an Energy Minimization Principle. We extend their definition and show the Energy Minimization Principle for general smooth projective curves. As an application we get a generalization and a different proof of an equidistribution result by Baker and Petsche.

v2: added citations of Charles Favre, Mattias Jonsson and Juan Rivera-Letelier, which unfortunately were missed in the first version, other minor changes, 31 pages