We show that a second main theorem of Nevanlinna theory holds for meromorphic functions on general complete Kähler manifolds. It is well-known in classical Nevanlinna theory that a meromorphic function whose image grows rapidly enough can omit at most two points. Our second main theorem implies this fact holds for meromorphic functions on general complete Kähler manifolds.
Publié le : 2008-04-15
Classification:
Nevanlinna theory,
Brownian motion on Kähler manifolds,
Kähler diffusion,
value distribution theory for meromorphic functions,
32H30,
58J65
@article{1212156659,
author = {ATSUJI, Atsushi},
title = {A second main theorem of Nevanlinna theory for meromorphic functions on complete K\"ahler manifolds},
journal = {J. Math. Soc. Japan},
volume = {60},
number = {1},
year = {2008},
pages = { 471-493},
language = {en},
url = {http://dml.mathdoc.fr/item/1212156659}
}
ATSUJI, Atsushi. A second main theorem of Nevanlinna theory for meromorphic functions on complete Kähler manifolds. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp. 471-493. http://gdmltest.u-ga.fr/item/1212156659/