Related papers: On Cartan's second main theorems for holomorphic c…
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…
The possibility of reversion of the inequality in the Second Main Theorem of Cartan in the theory of holomorphic curves in projective space is discussed. A new version of this theorem is proved that becomes an asymptotic equality for a…
In this paper, we establish a second main theorem for holomorphic curve intersecting hypersurfaces in general position in projective space with level of truncation. As an application, we reduce the number hypersurfaces in uniqueness problem…
In 1983, Nochka proved a conjecture of Cartan on defects of holomorphic curves in CP^n relative to a possibly degenerate set of hyperplanes. In this paper, we generalize the Nochka's theorem to the case of curves in a complex projective…
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.
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…
In this paper, we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces (totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex…
We describe some results of value distribution theory of holomorphic curves and quasiregular maps, which are obtained using potential theory. Among the results discussed are: extensions of Picard's theorems to quasiregular maps between…
A generalization of the second main theorem of tropical Nevanlinna theory is presented for noncontinuous piecewise linear functions and for tropical hypersurfaces without requiring a growth condition. The method of proof is novel and…
Let $\{D_i\}_{i=1}^{n+1}$ be $n+1$ hypersurfaces in $\mathbb{P}^n(\mathbb{C})$ with total degrees $\sum_{i=1}^{n+1} \deg D_i\geqslant n+2$, in general position and satisfying a generic geometric condition: every $n$ hypersurfaces intersect…
We consider a problem of whether a property of holomorphic curves on a subset $X$ of the complex plane can be extended to the whole complex plane. In this paper, the property we consider is uniqueness of holomorphic curves. We introduce the…
In this article, we mainly obtain the Riemann-Hurwitz theorems for harmonic morphisms on (vertex-weighted) metric graphs or metrized complexes of algebraic curves, inspired of the recent work on harmonic morphisms of graphs or metrized…
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…
We propose a new approach to the value distribution theory of entire holomorphic curves. We define a ``packing density'' of an entire holomorphic curve, and show that it has various non-trivial properties. We prove a ``gap theorem'' for…
In this paper, we prove a lemma on logarithmic derivative for holomorphic curves from annuli into K\"{a}hler compact manifold and. As its application, a second main theorem for holomophic curves from annuli into semi abelian varieties…
By means of $C^\infty$-connections we will prove a general second main theorem and some special ones for holomorphic curves. The method gives a geometric proof of H. Cartan's second main theorem in 1933. By applying the same method, we will…
We establish second main theorems for holomorphic curves into a projective subvary $V \subset \mathbb{P}^n(\mathbb{C})$ of dimension $k$, intersecting hypersurfaces in $N$-subgeneral position with respect to $V$ $(N > k)$. Our results…
In this paper, we prove some difference analogue of second main theorems of meromorphic mapping from Cm into an algebraic variety V intersecting a finite set of fixed hypersurfaces in subgeneral position. As an application, we prove a…
In [Ann. of Math. 169 (2009)], Min Ru proved a second main theorem for algebraically nondegenerate holomorphic curves in complex projective varieties intersecting fixed hypersurface targets. In this paper, by introducing a new proof method…
We generalize the H. Cartan's theory of holomorphic curves for a general open Riemann surface. Besides, a vanishing theorem for jet differentials and a Bloch's theorem for Riemann surfaces are obtained.