Indicatrix of Invariant metrics, Maximal circularity and Scaling of domains

Abstract

We investigate how to use the indicatrix of an invariant metric to rescale a sequence of biholomorphic maps and to ensure the convergence of the rescaled sequence. We also use the indicatrix of the Kobayashi-Royden metric to define the maximal circularity function which indicates how the domain is close to a circular domain.