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In this short manuscript, we will put some light on the different outcomes when two non-constant meromorphic functions share a value with prescribed weight two.

Complex Variables · Mathematics 2024-03-27 Sudip Saha , Amit Kumar Pal , Soumon Roy

The purpose of this paper is to obtain some sufficient conditions to determine the relation between a meromorphic function and an L-function when certain differential polynomial generated by them sharing a one degree polynomial. The main…

Complex Variables · Mathematics 2020-08-24 Abhijit Banerjee , Saikat Bhattacharyya

We consider links of complex isolated hypersurface singularities in $\mathbb{C}^{n+1}$ and study differentiable maps defined by restricting holomorphic functions to the links. We give an explicit example in which such a restriction gives a…

Geometric Topology · Mathematics 2024-02-06 Osamu Saeki , Shuntaro Sakurai

In this paper, we investigate meromorphic solutions in $\mathbb{C}^m$ of the nonlinear differential equation \[\displaystyle f^n\partial_u(f)g^n\partial_u(g)=1,\] where $\partial_u(f)=\sum_{j=1}^mu_j\partial_j(f)$ and $\sum_{j=1}^m u_j\neq…

Complex Variables · Mathematics 2025-11-14 Abhijit Banerjee , Sujoy Majumder , Debabrata Pramanik , Nabadwip Sarkar

In this article, we prove that there are at most two meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)\ (n\geqslant 2)$ sharing $2n+2$ hyperplanes in general position regardless of multiplicity, where all zeros with…

Complex Variables · Mathematics 2019-02-27 Si Duc Quang

Let $M\subset \mathbb C^n$ be a real analytic hypersurface, $M'\subset \mathbb C^N$ $(N\geq n)$ be a strongly pseudoconvex real algebraic hypersurface of the special form and $F$ be a meromorphic mapping in a neighborhood of a point $p\in…

Complex Variables · Mathematics 2020-02-28 Ozcan Yazici

Nevanlinna showed that two non-constant meromorphic functions on $\mathbb C$ must be linked by a M\"{o}bius transformation if they have the same inverse images counted with multiplicities for four distinct values. After that this results is…

Complex Variables · Mathematics 2015-01-20 Si Duc Quang , Le Ngoc Quynh

We present some results on two meromorphic functions from S to the Riemann sphere sharing a number of values where S is a Riemann surface of one of the following types: compact, compact minus finitely many points, the unit disk, a torus,…

Complex Variables · Mathematics 2016-10-05 Andreas Schweizer

In this paper, we give a simple proof and strengthening of a uniqueness theorem of meromorphic functions which partially share 0, $\infty$ CM and 1 IM with their difference operators. Meanwhile, we partial solve a conjecture given by…

Complex Variables · Mathematics 2021-01-05 Feng Lü , Zhenliu Yang

In the work, we focus on a conjecture due to Z.X. Chen and H.X. Yi[1] which is concerning the uniqueness problem of meromorphic functions share three distinct values with their difference operators. We prove that the conjecture is right for…

Complex Variables · Mathematics 2015-04-14 Feng Lü , Weiran Lü

In this article, we establish some new second main theorems for meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ and moving hyperplanes with truncated counting functions. Our results are improvements of the previous…

Complex Variables · Mathematics 2019-02-27 Si Duc Quang

This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…

Differential Geometry · Mathematics 2012-05-01 Aaron M. Smith

The purpose of this paper is to prove the finiteness theorems for meromorphic mappings of a complete connected K\"{a}hler manifold into projective space sharing few hyperplanes in subgeneral position without counting multiplicity, where all…

Complex Variables · Mathematics 2020-03-10 Thoan Pham Duc , Tuyen Nguyen Dang , Vangty Noulorvang

The 4IM+1CM problem is determining all pairs (f,g) of meromorphic functions in the complex plane that are not Moebius transformations of each other and share five pairs of complex values, one of them counting multiplicities. It is shown…

Complex Variables · Mathematics 2024-10-03 Norbert Steinmetz

Replaced by a shorter version which appeared in press.

Complex Variables · Mathematics 2017-01-23 S. Ivashkovich , F. Meylan

In this paper we have mainly focused on the uniqueness of two meromorphic functions under the realm of two shared sets problem with certain restrictions which in turn improve the results of { P. Sahoo and H. Karmakar, Uniqueness theorems…

Complex Variables · Mathematics 2020-09-01 Abhijit Banerjee , Saikat Bhattacharyya

In this paper, we examine holomorphic Segre preserving maps between the complexifications of real hypersurfaces in $\mathbb{C}^{n+1}$. In particular, we find several sufficient conditions ensuring that Segre transversality and total Segre…

Complex Variables · Mathematics 2008-10-16 R. Blair Angle

The purpose of this article has two fold. The first is to generalize some recent second main theorems for the mappings and moving hyperplanes of $\P^n(\C)$ to the case where the counting functions are truncated multiplicity (by level $n$)…

Complex Variables · Mathematics 2019-02-13 Duc Thoan Pham , Hai Nam Nguyen , Van An Nguyen

In this study, multivalued generalizations of certain classes of single-valued transformations defined on metric spaces are obtained. Building upon recently introduced concepts such as mappings contracting perimeters of triangles, new…

Functional Analysis · Mathematics 2025-05-06 Emirhan Hacioğlu

In this paper, we consider holomorphic mappings between real hypersurfaces in different dimensional complex spaces. We give a number of conditions that imply that such mappings are transversal to the target hypersurface at most points.

Complex Variables · Mathematics 2007-05-23 M. S. Baouendi , Peter Ebenfelt , Linda P. Rothschild