A Space of Meromorphic Mappings and an Elimination of Defects

This is a summary report of my recent articles. Nevanlinna theory asserts that each meromorphic mapping f of C into P(C) has few defects. However, it seems that meromorphic mappings with defects are very few. In this report, we shall show that for any given transcendental meromorphic mapping of C into P(C); there is a small deformation of f which has no Nevanlinna deficient hyperplanes in Pn(C); and also in the case m = 1; there is a small deformation of f which has no Nevanlinna deficient hypersurfaces of degree · d for each given positive integer d; or deficient rational moving targets. Furthermore, we shall show that mappings without Nevanlinna defects are dense in a space of transcendental meromorphic mappings.