Energy Minimization Principle for non-archimedean curves

TL;DR

This paper extends the Energy Minimization Principle for Arakelov-Green's functions from the projective line to general smooth projective curves, providing new proofs and generalizations of equidistribution results.

Contribution

It generalizes the Energy Minimization Principle to all smooth projective curves and offers a new proof of an existing equidistribution theorem.

Findings

Energy Minimization Principle holds for general smooth projective curves

Provides a new proof of Baker and Petsche's equidistribution result

Extends Arakelov-Green's functions to broader settings

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.