Nagoya Mathematical Journal

Moduli space of Brody curves, energy and mean dimension

Masaki Tsukamoto

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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.

Article information

Nagoya Math. J., Volume 192 (2008), 27-58.

First available in Project Euclid: 22 December 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32H30: Value distribution theory in higher dimensions {For function- theoretic properties, see 32A22}

moduli space of Brody curves mean dimension mean energy the Nevanlinna theory


Tsukamoto, Masaki. Moduli space of Brody curves, energy and mean dimension. Nagoya Math. J. 192 (2008), 27--58.

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