Brody curves and mean dimension

Matsuo, Shinichiroh¹ ; Tsukamoto, Masaki²

¹ Department of Mathematics, Osaka University, Toyonaka, Osaka 560-0043, Japan
² Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan

Journal of the American Mathematical Society, Tome 28 (2015) no. 1, pp. 159-182

Résumé

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.

Détail

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

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