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A class of functions containing polyharmonic functions in ℝⁿ

V. Anandam, M. Damlakhi (2003)

Annales Polonici Mathematici

Some properties of the functions of the form v ( x ) = i = 0 m | x | i h i ( x ) in ℝⁿ, n ≥ 2, where each h i is a harmonic function defined outside a compact set, are obtained using the harmonic measures.

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 .

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.

Ensembles pics pour A ( D )

Jacques Chaumat, Anne-Marie Chollet (1979)

Annales de l'institut Fourier

Soit D un domaine borné strictement pseudoconvexe dans C n à frontière régulière D . On montre que tout compact d’une sous-variété N de D dont l’espace tangent T p ( N ) en chaque point p de N est contenu dans le sous-espace complexe maximal de T p ( D ) est un ensemble pic pour A ( D ) , la classe des fonctions analytiques dans D dont toutes les dérivées sont continues dans D .

Hyperbolic-like manifolds, geometrical properties and holomorphic mappings

Grzegorz Boryczka, Luis Tovar (1996)

Banach Center Publications

The authors are dealing with the Dirichlet integral-type biholomorphic-invariant pseudodistance ρ X α ( z 0 , z ) [ ] introduced by Dolbeault and Ławrynowicz (1989) in connection with bordered holomorphic chains of dimension one. Several properties of the related hyperbolic-like manifolds are considered remarking the analogies with and differences from the familiar hyperbolic and Stein manifolds. Likewise several examples are treated in detail.

Limit currents and value distribution of holomorphic maps

Daniel Burns, Nessim Sibony (2012)

Annales de l’institut Fourier

We construct d -closed and d d c -closed positive currents associated to a holomorphic map φ 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.

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