Amoebas, Ronkin function and Monge-Ampère measures of algebraic curves with marked points

Abstract

A generalization of the amoeba and the Ronkin function of a plane algebraic curve for a pair of harmonic functions on an algebraic curve with punctures is proposed. Extremal properties of $M$-curves are proved and connected with the spectral theory of difference operators with positive coefficients.

Latex, 15 pages