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Brody curves and mean dimension


Authors: Shinichiroh Matsuo and Masaki Tsukamoto
Journal: J. Amer. Math. Soc. 28 (2015), 159-182
MSC (2010): Primary 32H30, 54H20
DOI: https://doi.org/10.1090/S0894-0347-2014-00798-0
Published electronically: May 22, 2014
MathSciNet review: 3264765
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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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Shinichiroh Matsuo
Affiliation: Department of Mathematics, Osaka University, Toyonaka, Osaka 560-0043, Japan
Email: matsuo@math.sci.osaka-u.ac.jp

Masaki Tsukamoto
Affiliation: Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
Email: tukamoto@math.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/S0894-0347-2014-00798-0
Keywords: Brody curve, mean dimension, deformation theory
Received by editor(s): June 28, 2012
Received by editor(s) in revised form: January 6, 2014
Published electronically: May 22, 2014
Article copyright: © Copyright 2014 American Mathematical Society