An extension of the theorem of Steinmetz-Nevanlinna to holomorphic curves
In 1929 R. Nevanlinna conjectured that his famous defect relation remains valid for slow moving target functions. After a series of partial results and complicated proofs, N. Steinmetz succeeded in 1986 with a short and elegant proof. His method is based on previous work of Chi-Tai Chuang (1964) and G. Frank and G. Weissenborn (1986), while the difficult proof of Ch. F. Osgood (1985) uses methods of diophantian approximation. In this paper, the analogous conjecture for holomorphic curves \(f: {\mathbb{C}}\to {\mathbb{P}}_ n\) is studied where the target hyperplanes move slowly relative to f. A defect relation with defect bound \(n(n+1)\) is obtained, which coincides with the Steinmetz result if \(n=1\), but does not attain the conjectured bound \(n+1\) if \(n>1\).
scientific article; zbMATH DE number 4023655
scientific article