Related papers: Unicity problem on meromorphic mappings of complet…
The paper develops an equidistribution theory of meromorphic mappings from a complete K\"ahler manifold with non-negative Ricci curvature into a complex projective manifold intersecting normal crossing divisors. When the domain manifolds…
Nevanlinna's five-value theorem is well-known as a famous theorem in value distribution theory, which asserts that two non-constant meromorphic functions on $\mathbb C$ are identical if they share five distinct values ignoring…
In this paper, we generalize the classical Nevanlinna theory of algebroid functions from $\mathbb C$ to a complete K\"ahler manifold with either non-negative Ricci curvature or non-positive sectional curvature. As its applications, we…
We study Nevanlinna theory on complete K\"ahler manifolds. As a consequence of the main result, we prove a defect relation of holomorphic mappings from complete K\"ahler manifolds of non-positive sectional curvature into complex projective…
We consider the classical Picard's problem for non-parabolic complete K\"ahler manifolds with non-negative Ricci curvature. Based on the global Green function approach, we give a positive answer to Picard's problem under certain condition…
The classical result of Nevanlinna states that two nonconstant meromorphic functions on the complex plane having the same images for five distinct values must be identically equal to each other. In this paper, we give a similar uniqueness…
The purpose of this paper has twofold. The first is to prove a unicity theorem for meromorphic mappings of a complete K\"{a}hler manifold M in P^n(C) sharing few hypersurfaces. The second is to give a unicity theorem for the case of…
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…
This work continues the author's earlier work (2026, Studia Mathematica) on Picard's problem: is every meromorphic function on a complete noncompact K\"ahler manifold with nonnegative Ricci curvature necessarily a constant, if it avoids 3…
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…
Theorem (uniformization). Let X be a compact Kahler manifold of dimension n with large, residually finite and nonamenable fundamental group. Then its universal covering is a bounded domain in the n-dimensional affine space.
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 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…
Nevanlinna's second main theorem is a far-reaching generalisation of Picard's Theorem concerning the value distribution of an arbitrary meromorphic function f. The theorem takes the form of an inequality containing a ramification term in…
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…
The purpose of this article is threefold. The first is to construct a Nevanlina theory for meromorphic mappings from a polydisc to a compact complex manifold. In particular, we give a simple proof of Lemma on logarithmic derivative for…
A two-parameter characteristic of functions meromorphic on annuli is introduced and an extension of the Nevanlinna value distribution theory for such functions is proposed.
In this paper, we study several types of geometric problems related to the Ricci curvature on noncompact complex manifolds, such as the existence of K\"{a}hler-Einstein metrics on complete K\"{a}hler manifolds with negative Ricci curvature,…
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…
In this paper, by combining techniques from Ricci flow and algebraic geometry, we prove the following generalization of the classical uniformization theorem of Riemann surfaces. Given a complete noncompact complex two dimensional K\"ahler…