Le problème du complémentaire d'une hypersurface holomorphe en analyse hyperbolique.
L'image d'une application holomorphe
Limit currents and value distribution of holomorphic maps
We construct -closed and -closed positive currents associated to a holomorphic map via cluster points of normalized weighted truncated image currents. They are constructed using analogues of the Ahlfors length-area inequality in higher dimensions. Such classes of currents are also referred to as Ahlfors currents. We give some applications to equidistribution problems in value distribution theory.
Multiple values and uniqueness problem for meromorphic mappings sharing hyperplanes
The purpose of this article is to deal with multiple values and the uniqueness problem for meromorphic mappings from into the complex projective space ℙⁿ(ℂ) sharing hyperplanes. We obtain two uniqueness theorems which improve and extend some known results.
Nevanlinna Defect Relations for Singular Divisors.
Normal families of meromorphic mappings of several complex variables into ℂPⁿ for moving hypersurfaces
We prove some normality criteria for families of meromorphic mappings of a domain into ℂPⁿ under a condition on the inverse images of moving hypersurfaces.
On fundamental groups of algebraic varieties and value distribution theory
If a smooth projective variety admits a non-degenerate holomorphic map from the complex plane , then for any finite dimensional linear representation of the fundamental group of the image of this representation is almost abelian. This supports a conjecture proposed by F. Campana, published in this journal in 2004.
On meromorphic functions with maximal defect sum
The purpose of this article is twofold. The first is to give necessary conditions for the maximality of the defect sum. The second is to show that the class of meromorphic functions with maximal defect sum is very thin in the sense that deformations of meromorphic functions with maximal defect sum by small meromorphic functions are not meromorphic functions with maximal defect sum.
On Nevanlinna's second main theorem in projective space.
On the uniqueness problem for meromorphic mappings with truncated multiplicities
The purpose of this paper is twofold. The first is to weaken or omit the condition for i ≠ j in some previous uniqueness theorems for meromorphic mappings. The second is to decrease the number q of hyperplanes such that f(z) = g(z) on , where f,g are meromorphic mappings.
Parabolic exhaustions and analytic coverings.
Ramification of the Gauss map of complete minimal surfaces in on annular ends
We study the ramification of the Gauss map of complete minimal surfaces in on annular ends. This is a continuation of previous work of Dethloff-Ha (2014), which we extend here to targets of higher dimension.
Schottky-Landau growth estimates for s-normal families of holomorphic mappings.
Singularités des courants d'Ahlfors
Sur une minoration du degré d'hypersurfaces s'annulant en certains points.
The dimensions of integral points and holomorphic curves on the complements of hyperplanes
The growth of regular functions on algebraic sets
We are concerned with the set of all growth exponents of regular functions on an algebraic subset V of . We show that its elements form an increasing sequence of rational numbers and we study the dependence of its structure on the geometric properties of V.
The second main theorem for algebroid functions.
Un théorème de Bloch presque complexe
Cet article est consacré à la démonstration d’une version presque complexe du théorème de Bloch. Considérons la réunion C de quatre J-droites en position générale dans un plan projectif presque complexe. Nous démontrons que toute suite non normale de J-disques évitant évitant la configuration C admet une sous-suite convergeant, au sens de Hausdorff, vers une partie la réunion des diagonales de C. En particulier, le complémentaire de la configuration C est hyperboliquement plongé dans le paln projectif...
Unicity of meromorphic mappings sharing few hyperplanes
We prove some theorems on uniqueness of meromorphic mappings into complex projective space ℙⁿ(ℂ), which share 2n+3 or 2n+2 hyperplanes with truncated multiplicities.