An extension of Fujimoto's non-integrated defect relation in Nevanlinna theory from holomorphic maps into complex projective space to non-constant holomorphic maps from a complete open Riemann surface into an arbitrary smooth projective variety. The non-integrated defect with respect to an effective Cartier divisor D and an ample divisor A is defined through the existence of a bounded continuous function making a current inequality in the first Chern forms hold; the paper proves the corresponding Second-Main-Theorem-type defect relation under the hypothesis that a Green-Griffiths k-jet differential vanishes on the divisor components.
A result in Nevanlinna theory (value distribution theory) that generalizes Fujimoto's non-integrated defect relation from maps into complex projective space to maps into arbitrary smooth projective v…