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Ahlfors’ currents in higher dimension

Henry de Thélin (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

We consider a nondegenerate holomorphic map f : V ↦ X where ( X , ω ) is a compact Hermitian manifold of dimension larger than or equal to k and V is an open connected complex manifold of dimension k . In this article we give criteria which permit to construct Ahlfors’ currents in X .

An extension of Schwick's theorem for normal families

Yasheng Ye, Xuecheng Pang, Liu Yang (2015)

Annales Polonici Mathematici

In this paper, the definition of the derivative of meromorphic functions is extended to holomorphic maps from a plane domain into the complex projective space. We then use it to study the normality criteria for families of holomorphic maps. The results obtained generalize and improve Schwick's theorem for normal families.

Classes de Nevanlinna sur une intersection d'ouverts strictement pseudoconvexes.

Chantal Menini (1995)

Publicacions Matemàtiques

On a finite intersection of strictly pseudoconvex domains we define two kinds of natural Nevanlinna classes in order to take the growth of the functions near the sides or the edges into account. We give a sufficient Blaschke type condition on an analytic set for being the zero set of a function in a given Nevanlinna class. On the other hand we show that the usual Blaschke condition is not necessary here.

Degeneracy of holomorphic maps via orbifolds

Erwan Rousseau (2012)

Bulletin de la Société Mathématique de France

We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal surfaces and complements of singular plane curves.

Distribution des préimages et des points périodiques d’une correspondance polynomiale

Tien-Cuong Dinh (2005)

Bulletin de la Société Mathématique de France

Nous construisons pour toute correspondance polynomiale F d’exposant de Lojasiewicz ℓ > 1 une mesure d’équilibre μ . Nous montrons que μ est approximable par les préimages d’un point générique et que les points périodiques répulsifs sont équidistribués sur le support de μ . En utilisant ces résultats, nous donnons une caractérisation des ensembles d’unicité pour les polynômes.

Distribution laws for integrable eigenfunctions

Bernard Shiffman, Tatsuya Tate, Steve Zelditch (2004)

Annales de l’institut Fourier

We determine the asymptotics of the joint eigenfunctions of the torus action on a toric Kähler variety. Such varieties are models of completely integrable systems in complex geometry. We first determine the pointwise asymptotics of the eigenfunctions, which show that they behave like Gaussians centered at the corresponding classical torus. We then show that there is a universal Gaussian scaling limit of the distribution function near its center. We also determine the limit...

Finiteness of meromorphic functions on an annulus sharing four values regardless of multiplicity

Duc Quang Si, An Hai Tran (2020)

Mathematica Bohemica

This paper deals with the finiteness problem of meromorphic funtions on an annulus sharing four values regardless of multiplicity. We prove that if three admissible meromorphic functions f 1 , f 2 , f 3 on an annulus 𝔸 ( R 0 ) share four distinct values regardless of multiplicity and have the complete identity set of positive counting function, then f 1 = f 2 or f 2 = f 3 or f 3 = f 1 . This result deduces that there are at most two admissible meromorphic functions on an annulus sharing a value with multiplicity truncated to level 2 and...

Hyperbolicity and integral points off divisors in subgeneral position in projective algebraic varieties

Do Duc Thai, Nguyen Huu Kien (2015)

Acta Arithmetica

The purpose of this article is twofold. The first is to find the dimension of the set of integral points off divisors in subgeneral position in a projective algebraic variety V ⊂ ℙ k ̅ m , where k is a number field. As consequences, the results of Ru-Wong (1991), Ru (1993), Noguchi-Winkelmann (2003) and Levin (2008) are recovered. The second is to show the complete hyperbolicity of the complement of divisors in subgeneral position in a projective algebraic variety V ⊂ ℙ ℂ m .

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