Brody curves and mean dimension

Matsuo, Shinichiroh; Tsukamoto, Masaki

doi:10.1090/S0894-0347-2014-00798-0

Brody curves and mean dimension
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by Shinichiroh Matsuo and Masaki Tsukamoto

J. Amer. Math. Soc. 28 (2015), 159-182

DOI: https://doi.org/10.1090/S0894-0347-2014-00798-0

Published electronically: May 22, 2014

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Abstract:

We study the mean dimensions of the systems of Brody curves. In particular we give the formula of the mean dimension of the system of Brody curves in the Riemann sphere. A key notion is a non-degeneracy of Brody curves introduced by Yosida (1934). We develop a deformation theory of non-degenerate Brody curves and apply it to the calculation of the mean dimension. Moreover we show that there are sufficiently many non-degenerate Brody curves by using the method of gluing infinitely many rational curves.

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