A version of the Schwarz lemma for correspondences is studied. Two applications are obtained namely, the 'non-increasing' property of the Kobayashi metric under correspondences and a weak version of the Wong-Rosay theorem for convex, finite type domains admitting a 'non-compact' family of proper correspondences.
In this paper, the definition of the derivative of meromorphic functions is extended to holomorphic maps from a plane domain into the complex projective space. We then use it to study the normality criteria for families of holomorphic maps. The results obtained generalize and improve Schwick's theorem for normal families.
Some known localization results for hyperconvexity, tautness or -completeness of bounded domains in are extended to unbounded open sets in .
We prove some normality criteria for families of meromorphic mappings of a domain into ℂPⁿ under a condition on the inverse images of moving hypersurfaces.