A SPACE OF MEROMORPHIC MAPPINGS AND AN ELIMINATION OF DEFECTS

Abstract

This is a summary report of my recent articles. Nevanlinna theory asserts that each meromorphic mapping f of Cm into Pn(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 Cm into Pn(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.