کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5774697 | 1413564 | 2018 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Exceptional values of holomorphic functions. Remarks on a Nishino's Theorem
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let F(z,w)âO(Cn+1), where (z,w)âCnÃC. Let zâ²âCn such that F(zâ²,w) is not constant. If F(zâ²,w) is not surjective it takes all the values of C minus one Ï(zâ²) (Picard). T. Nishino studied in [8] Ï(z) when n=1, F(z,w) is of finite order in w and Ï(z) is defined in a set EâC with at least one accumulation point. In this work, we see that his result allows to obtain an explicit expression of such a F(z,w) when nâ¥1 and F(zâ²,w) is not a constant for any zâ²âCn, and conclude that Ï(z)=η(z)â1/ξ(z) for η(z) and ξ(z)âO(Cn) when Ï(z) is defined on a nonempty open set UâCn. Moreover, we give several applications of this fact. We show that the complement of the graph of Ï(z) in Cn+1 is dominated by Cn+1 via a family of surjective fiber-preserving holomorphic maps with non-vanishing Jacobian determinant, which are described in terms of the flow of a complete vector field of type Câ. In particular, Buzzard and Lu's results in [2] applied to Ï(z) for n=1 can be extended for nâ¥2. It will allow to define new examples of Oka manifolds.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 457, Issue 1, 1 January 2018, Pages 1007-1014
Journal: Journal of Mathematical Analysis and Applications - Volume 457, Issue 1, 1 January 2018, Pages 1007-1014
نویسندگان
Alvaro Bustinduy,