2011/10/27 by Da Costa, Bernardo Freitas Paulo
#Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1110.6082
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.