Deformation of Brody curves and mean dimension

The main purpose of this paper is to show that ideas of deformation theory can be applied to infinite-dimensional geometry. We develop the deformation theory of Brody curves. A Brody curve is a kind of holomorphic map from the complex plane to the projective space. Since the complex plane is not compact, the parameter space of the deformation can be infinite-dimensional. As an application we prove a lower bound on the mean dimension of the space of Brody curves.