The stars at infinity in several complex variables

Abstract

This text reviews certain notions in metric geometry that may have further applications to problems in complex geometry and holomorphic dynamics in several variables. The discussion contains a few new results and formulates a number of questions related to the asymptotic geometry and boundary estimates of bounded complex domains, boundary extensions of biholomorphisms, the dynamics of holomorphic self-maps, Teichmüller theory, and the existence of constant scalar curvature metrics on compact Kähler manifolds.