A class of functions containing polyharmonic functions in ℝⁿ
Some properties of the functions of the form in ℝⁿ, n ≥ 2, where each is a harmonic function defined outside a compact set, are obtained using the harmonic measures.
A hypersurface defect relation for a family of meromorphic maps on a generalized p-parabolic manifold
This paper establishes a hypersurface defect relation, that is, , for a family of meromorphic maps from a generalized p-parabolic manifold M to the projective space ℙⁿ, under some weak non-degeneracy assumptions.
A p-adic Nevanlinna-Diophantine correspondence
Abschätzungen für die Anzahl der holomorphen Abbildungen zwischen algebraischen Räumen.
Ahlfors’ currents in higher dimension
We consider a nondegenerate holomorphic map where is a compact Hermitian manifold of dimension larger than or equal to and is an open connected complex manifold of dimension . In this article we give criteria which permit to construct Ahlfors’ currents in .
Anwendungen des Satzes von Picard.
Big Picard theorems for holomorphic mappings into the complement of moving hypersurfaces in .
Degeneracy of entire curves in log surfaces with
We determine which algebraic surface of logarithmic irregularity admit an algebraically non-degenerate entire curve.
Degeneracy of holomorphic maps via orbifolds
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.
Degeneracy of Holomorphic Maps with Ramification.
Diophantine approximations and foliations
Endlichkeits- und Picard-Sätze für quasiprojektive Räume.
Ensembles pics pour
Soit un domaine borné strictement pseudoconvexe dans à frontière régulière . On montre que tout compact d’une sous-variété de dont l’espace tangent en chaque point de est contenu dans le sous-espace complexe maximal de est un ensemble pic pour , la classe des fonctions analytiques dans dont toutes les dérivées sont continues dans .
Higher-Dimensional Analogues of Inoue-Hirzebruch Surfaces.
Holomorphe Abbildungen zwischen quasiprojektiven Räumen.
Hyperbolically Imbedded Spaces and the Big Picard Theorem.
Hyperbolic-like manifolds, geometrical properties and holomorphic mappings
The authors are dealing with the Dirichlet integral-type biholomorphic-invariant pseudodistance 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.
Integrals for holomorphic foliations with singularities having all leaves compact
We show that for a holomorphic foliation with singularities in a projective variety such that every leaf is quasiprojective, the set of rational functions that are constant on the leaves form a field whose transcendence degree equals the codimension of the foliation.
Irreducible identity sets for polynomial autormorphisms.
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.