DEUX EXEMPLES ON THE MEDIUM DIMENSION OF A SPACE OF BRODY CURVES

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.