On a Kobayashi hyperbolic manifold N modulo a closed subset ΔN and its applications

Abstract

We show that the degeneration locus of the Kobayashi pseudodistance on a complex manifold is always a pseudoconcave set of order 1. We give some results cocerning the degeneration locus of the Kobayashi pseudodistance. Next we prove a generalization of the little Picard theorem relevantly. Finally, we consider the case N = Δ_N.