Related papers: Tropical second main theorem and the Nevanlinna in…
We present a version of the tropical Nevanlinna theory for real-valued, continuous, piecewise linear functions on the real line. In particular, a tropical version of the second main theorem is proved. Applications to some ultra-discrete…
The tropical Nevanlinna theory is Nevanlinna theory for tropical functions or maps over the max-plux semiring by using the approach of complex analysis. The main purpose of this paper is to study the second main theorem with tropical…
Tropical Nevanlinna theory, introduced by Halburd and Southall as a tool to analyze integrability of ultra-discrete equations, studies the growth and complexity of continuous piecewise linear real functions. The purpose of this paper is to…
The main goal of this paper is to establish the higher-dimensional Nevanlinna theory in tropical geometry. We first develop a theory of tropical meromorphic functions ( holomorphic maps) in several variables, such as the proximity function,…
In this paper, the tropical Nevanlinna theory is extended for piecewise polynomial continuous functions. By constructing the $n$-th Poisson-Jensen formula, the $n$-th tropical counting, proximity, and characteristic functions are…
We prove a tropical analogue of Cartan's second main theorem for holomorphic curves intersecting hyperplanes in general position--a setting that was not fully resolved by previous tropical Nevanlinna theory. Two versions are obtained. The…
A tropical version of Nevanlinna theory is described in which the role of meromorphic functions is played by continuous piecewise linear functions of a real variable whose one-sided derivatives are integers at every point. These functions…
Tropical Nevanlinna theory studies value distribution of continuous piecewise linear functions of a real variable. In this paper, we use the reasoning from tropical Nevanlinna theory to present tropical counterparts of some classical…
We develop Nevanlinna's theory for a class of holomorphic maps when the source is a disc. Such maps appear in the theory of foliations by Riemann Surfaces.
We study Nevanlinna theory of meromorphic mappings from a geodesic ball of a general complete K\"ahler manifold with non-negative Ricci curvature into a complex projective manifold by introducing a heat kernel method. When dimension of a…
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…
How to devise a second main theorem with best error terms is a central problem in the study of Nevanlinna theory. However, it seems difficult to be done for a general non-positively curved K\"ahler manifold. Based on the work of A. Atsuji…
We study the Second Main Theorem in non-archimedean Nevanlinna theory, giving an improvement to the non-archimedean Second Main Theorems of Ru and An in the case where all the hypersurfaces have degree greater than one and all intersections…
In this paper, by introducing the notion of "\textit{distributive constant}" of a family of hypersurfaces with respect to a projective variety, we prove a second main theorem in Nevanlinna theory for meromorphic mappings with arbitrary…
We obtain a Second Main Theorem type inequality for holomorphic maps $f : M \to X$, where $M$ is a parabolic manifold and $X$ is smooth projective with dim $M$ $\le$ dim $X$. We also derive a parabolic Tautological inequality for smooth…
This paper has twofold. The first is to establish a second main theorem for meromorphic functions on the complex disc $\Delta (R_0)\subset\mathbb C$ with finite growth index and small functions, where the counting functions are truncated to…
Kapranov's theorem is a foundational result in tropical geometry. It states that the set of tropicalisations of points on a hypersurface coincides precisely with the tropical variety of the tropicalisation of the defining polynomial. The…
The purpose of this article is twofold. The first is to prove a second main theorem for meromorphic mappings of $\C^m$ into a complex projective variety intersecting hypersurfaces in subgeneral position with truncated counting functions.…
In this paper, we prove some fundamental theorems for holomorphic curves on angular domain intersecting a hypersurface, finite set of fixed hyperplanes in general position and finite set of fixed hypersurfaces in general position on complex…
This paper re-develops the Nevanlinna theory for meromorphic functions on $\mathbb C$ in the viewpoint of holomorphic forms. According to our observation, Nevanlinna's functions can be formulated by a holomorphic form. Applying this thought…