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Two examples on the mean dimension of spaces of Brody curves. (Deux exemples sur la dimension moyenne d’un espace de courbes de Brody.) (French. English summary) Zbl 1295.30083
Summary: We study the mean dimension of the space of 1-Brody curves lying in two complex surfaces: first for Hopf surfaces, then for the projective plane minus a line. We show in the first case that the mean dimension is zero via a bound on the growth of meromorphic curves involving the logarithmic derivative lemma. In the second case, we show its positivity by lifting from the line to its complement a space of Brody curves of positive mean dimension containing deformations of an elliptic curve.

30D45 Normal functions of one complex variable, normal families
32Q99 Complex manifolds
30D15 Special classes of entire functions of one complex variable and growth estimates
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