Moduli space of Brody curves, energy and mean dimension.

Masaki TSUKAMOTO

Brody curve is a holomorphic map from the complex line to a complex manifold with bounded derivative.
Since the complex line is not compact, the moduli space of Brody curves is infinite dimensional in general.
We study the Gromov mean dimension of the moduli space of Brody curves by using energy of Brody curves.
This is an attempt to evaluate the dimension of infinite dimensional space. Key words: Brody curve,
mean dimension, energy, the Nevanlinna theory