Moduli space of Brody curves, energy and mean dimension

Abstract

A Brody curve is a holomorphic map from the complex plane $\mathbb{C}$ to a Hermitian manifold with bounded derivative. In this paper we study the value distribution of Brody curves from the viewpoint of moduli theory. The moduli space of Brody curves becomes infinite dimensional in general, and we study its "mean dimension". We introduce the notion of "mean energy" and show that this can be used to estimate the mean dimension.