Related papers: Second main theorems for meromorphic mappings inte…
In this paper, we prove a second main theorem for a holomorphic curve $f$ into $\mathbb P^N (\mathbb C)$ with a family of slowly moving hypersurfaces $D_1,...,D_q$ with respect to $f$ in $m$-subgeneral position, proving an inequality with…
In this paper, we establish a new second main theorem for meromorphic functions on a non-Archimedean field and small functions with counting functions truncated to level $1.$ As an application, we show that two meromorphic functions on a…
We establish a Second Main Theorem for entire holomorphic curves \( f: \mathbb{C} \to \mathbb{P}^2 \) intersecting a generic configuration of three conics \(\mathcal{C}= \mathcal{C}_1+ \mathcal{C}_2+ \mathcal{C}_3 \) in the complex…
The purpose of this paper has twofold. The first is to establish a second main theorem for meromorphic functions on annuli and meromorphic function targets (may not be small functions) with truncated counting functions (truncation level 1)…
Let $M$ be a complete K\"{a}hler manifold, whose universal covering is biholomorphic to a ball $\mathbb B^m(R_0)$ in $\mathbb C^m$ ($0<R_0\le +\infty$). In this article, we will show that if three meromorphic mappings $f^1,f^2,f^3$ of $M$…
In this paper, we will show that if two meromorphic mappings $f$ and $g$ of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ have the same inverse images for $(2n+2)$ moving hyperplanes $\{a_i\}_{i=1}^{2n+2}$ with multiplicities counted to level…
Since the great work on holomorphic curves into algebraic varieties intersecting hypersurfaces in general position established by Ru in 2009, recently there has been some developments on the second main theorem into algebraic varieties…
In this paper, we study the uniqueness problem for linearly nondegenerate meromorphic mappings from a K\"{a}hler manifold into $\mathbb P^n(\mathbb C)$ satisfying a condition $(C_\rho)$ and sharing hyperplanes in general position, where the…
The main aim of this article is to give some sufficient conditions for a family of meromorphic mappings on a domain D in C^n into P^N(C) to be meromorphically normal if they satisfy only some very weak conditions with respect to moving…
In this paper, we give some extension of fundamental theorems in Nevanlinna - Cartan theory for holomorphic curve on M punctured complex planes. As an application, we establish a result for uniqueness problem of holomorphic curve by inverse…
We establish a second main theorem for algebraic tori with slow growth moving targets with truncation to level 1. As the first application of this result, we prove the Green-Griffith-Lang conjecture for projective spaces with $n+1$…
Let $M$ be a complete K\"{a}hler manifold, whose universal covering is biholomorphic to a ball $\mathbb B^m(R_0)$ in $\mathbb C^m$ ($0<R_0\le +\infty$). In this article, we will show that if three meromorphic mappings $f^1,f^2,f^3$ of $M$…
In this paper, on the basis of a specific question raised in [6], we further continue our investigations on the uniqueness of a meromorphic function with its higher derivatives sharing two sets and answer the question affirmatively.…
We proved a truncated second main theorem of level one with explicit exceptional sets for analytic maps into $\mathbb P^2$ intersecting the coordinate lines with sufficiently high multiplicities. As applications, we studied some cases of…
In this paper, we prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share three sets. The obtained results improve some recent existing results.
In this note, we introduce a new kind of pair of finite range sets in $\mathbb{C}$ for meromorphic functions corresponding to their uniqueness, i.e., how two meromorphic functions are uniquely determined by their two finite shared sets.
Let $ H_1,\dots,H_{2n+2}$ be \emph{generic} $(2n+2)$ hyperplanes in $\mathbb{P}^n.$ It is proved that if meromorphic maps $ f $ and $ g $ of $\mathbb{C}^m $ into $\mathbb{P}^n $ satisfy $ f^*(H_j)=g^*(H_j)$ $(1\leq j\leq 2n+2)$ and $ g $ is…
Following the definition of perturbed metric space, in this paper, some fixed point theorems are established for $ F $-perturbed mappings in complete perturbed metric spaces and justify the result by counter example. Finally, an application…
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…
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…