Nevanlinna theory

Value distribution theory of the Gauss map of complete regular minimal surfaces has a long history, in particular, much attention has been given to this theory from the viewpoint of the Nevanlinna theory. In this article, we will establish an estimate for the Gaussian curvature of minimal surfaces in R 4 whose classical Gauss map is ramified over the set of distinct points.

12p visharma 20-10-2023 3 2   Download

In the case of dimension one, this problem was studied by Lappan and Hinkkanen. The main purpose of this paper is to extend the result of Tan in to the case of hypersurface targets. Our result is also the counterpart of the result of Son and Tan in on the normality criterion of holomorphic mappings.

5p visharma 20-10-2023 7 2   Download

Using the second main theorem of value distribution theory and Borel’s lemma, Nevanlinna proved that for two nonconstant meromorphic functions \(f\) and \(g\) on the complex plane C, if they have the same inverse images for five distinct values, then \(f \equiv g\), and that \(g\) is a special type of linear fractional transformation of \(f\) if they have the same inverse images, counted with multiplicities, for four distinct values.

10p runordie5 04-07-2022 3 2   Download

Value distribution theory for holomorphic curves which also known as Nevanlinna-Cartan theory was originated by the work of H. Cartan in 1933. Since that time, it had attracted the attention of many mathematicians and had many important publications and it had many applications in different areas of mathematics.

8p vimarissamayer 02-06-2022 10 3   Download

In this paper, we establish a second main theorem with a good defect relation for entire curves in a projective variety whose derivatives vanish on inverse image of hypersurface targets. Our method is a combination of the techniques in [7-9].

10p koxih_kothogmih5 04-09-2020 16 2   Download

In this article, we use standard notations from the value distribution theory. We de-note the order of growth of f(z) by ÍT(/). In this paper, by using Nevanlinna theory, we study the growth the solution of differential equation.

8p vimessi2711 02-04-2019 21 1   Download

In this paper, we prove some normality criterias for two families meromorphic functions sharing sets and values related with above result. Up to now, our results are new.

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In this paper, we will consider the k-th derivative instead of the first derivative of the meromorphic functions. Thus, our work generalizes the related results due to Kamal Boussaf, Alain Escassut and Jacqueline Ojeda

7p vimessi2711 02-04-2019 8 0   Download

An extension of Nevanlinna value distribution theory for algebroid functions on annuli is proposed. The main characteristics are one-parameter and possess the same properties as in the classical case. Analogs of the Cartan theorem, the first fundamental theorem, the second fundamental theorem, deficient values, and the uniqueness of algebroid functions on annuli are proved.

20p danhdanh27 07-01-2019 17 2   Download

In this paper, we utilize Nevanlinna value distribution theory to study the uniqueness problem that a meromorphic function and its difference operator share two sets with weight k . Our results extend the previous results.

9p danhdanh27 07-01-2019 19 1   Download

Lars Ahlfors often spoke of his excitement as a young student listening to Rolf Nevanlinna's lectures on the new theory of meromorphic functions. It was, as he writes in his collected papers, his "first exposure to live mathematics." In his enormously influential research papers and in his equally influential books, Ahlfors shared with the reader, both professional and student, that excitement. The present volume derives from lectures given at Harvard over many years, and the topics would now be considered quite classical.

172p hotmoingay 04-01-2013 41 2   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Vấn đề Nevanlinna-Chọn cho ma trận có giá trị chức năng...

27p matuot_266 27-08-2011 48 4   Download