American Journal of Mathematical Analysis
ISSN (Print): 2333-8490 ISSN (Online): 2333-8431 Website: http://www.sciepub.com/journal/ajma Editor-in-chief: Grigori Rozenblum
Open Access
Journal Browser
Go
American Journal of Mathematical Analysis. 2015, 3(1), 19-20
DOI: 10.12691/ajma-3-1-4
Open AccessArticle

On the Analytic Curve of C2 which is not Omitted by Every Fatou-Bieberbach Domain

YUKINOBU ADACHI1,

1Yukinobu Adachi, Kurakuen, Nishinomiya, Hyogo, Japan

Pub. Date: February 06, 2015

Cite this paper:
YUKINOBU ADACHI. On the Analytic Curve of C2 which is not Omitted by Every Fatou-Bieberbach Domain. American Journal of Mathematical Analysis. 2015; 3(1):19-20. doi: 10.12691/ajma-3-1-4

Abstract

Let C be an irreducible (may be transendental) analytic curve whose genus is geater than 1. Then every Fatou-Bieberbach domain does not omit C.

Keywords:
fatou-bieberbach domain hyperbolic cuve transcendental algebraic type curve kobayashi hyperbolic

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Y. Adachi, A generalization of the big Picard theorem, Kodai Math. J., 18(1995), 408-424.
 
[2]  Y. Adachi, Remarks about Fatou-Bieberbach domains and algebraic or non-algebraic curves in C2, Far East J. Math. Soc. (FJMS), 34 (2009), 369-376.
 
[3]  Y. Adachi and Masakazu Suzuki, Degeneracy points of the Kobayashi pseudodistances on complex manifolds, Proceedings of Symposia in Pure Math., 52 (1991), Part 2, 41-51.
 
[4]  G. T. Buzzard and J. E. Fornaess, An embedding of C in C2 with hyperbolic complement, Math. Ann. 306 (1996), 539-546.
 
[5]  T. Nishino, Nouvelles recherches sur les fonctions entières de plusieurs variables conplexes (V) Fonctions qui se réduisent aux polynômes, J. Math. Kyoto Univ., 15 (1975), 527-553.
 
[6]  J. P. Rosay and W. Rudin, Holomorphic maps from Cn to Cn, Trans. A. M. S., 310 (1988), 47-86.