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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.

MSC:
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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