The Jacobian Conjecture: survey of some results
The paper contains the formulation of the problem and an almost up-to-date survey of some results in the area.
The linear fractional model on the ball.
The Lojasiewicz exponent at infinity for overdetermined polynomial mappings
We prove that the study of the Łojasiewicz exponent at infinity of overdetermined polynomial mappings , m > n, can be reduced to the one when m = n.
The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms
The second main theorem for algebroid functions.
The set of points at which a polynomial map is not proper
We describe the set of points over which a dominant polynomial map is not a local analytic covering. We show that this set is either empty or it is a uniruled hypersurface of degree bounded by .
The symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domains
We prove that the symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domains.
The theorem of Barth-Lefschetz as a consequence of Le Potier's vanishing theorem.
The theorem of Forelli for holomorphic mappings into complex spaces
Generalizations of the theorem of Forelli to holomorphic mappings into complex spaces are given.
Topology of Fatou components for endomorphisms of : linking with the Green’s current
Little is known about the global topology of the Fatou set U(f) for holomorphic endomorphisms , when k >1. Classical theory describes U(f) as the complement in of the support of a dynamically defined closed positive (1,1) current. Given any closed positive (1,1) current S on , we give a definition of linking number between closed loops in and the current S. It has the property that if lk(γ,S) ≠ 0, then γ represents a non-trivial homology element in . As an application, we use these linking...
Total geodesy of proper holomorphic immersions between complex hyperbolic space forms of finite volume.
Two Theorems on Extensions of Holomorphic Mappings.
Über Bilder projektiv-algebraischer Räume.
Über die Menge der kritischen Werte gewisser holomorpher Abbildungen.
Über ebene, faktorisierbare und einfache holomorphe Abbildungen.
Über einen Satz von Shl. Sternberg in der Theorie der analytischen Iterationen.
Über Einige Formale Aspekte Der Dynamik (Dividierbarkeit Und Analytische Iteration Kontrahierender Biholomorpher Abbildungen)
Über holomorphe Abbildungen mit projektiven Fasern.
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...
Un théorème de Green presque complexe
On montre l'hyperbolicité du complémentaire de cinq droites en position générale dans un plan projectif presque complexe, répondant ainsi à une question de S. Ivashkovich.