Indicatrix of invariant metrics, maximal circularity and scaling of domains

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.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

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