Der Kontinuitätssatz für reindimensionale &-affinoide Räume.
Elimination of defects of meromorphic mappings of into .
Extension and normality of meromorphic mappings into complex projective varieties
The purpose of this article is twofold. The first is to show a criterion for the normality of holomorphic mappings into Abelian varieties; an extension theorem for such mappings is also given. The second is to study the convergence of meromorphic mappings into complex projective varieties. We introduce the concept of d-convergence and give a criterion of d-normality of families of meromorphic mappings.
Hyperbolic measure of maximal entropy for generic rational maps of
Let be a dominant rational map of such that there exists with for all . Under mild hypotheses, we show that, for outside a pluripolar set of , the map admits a hyperbolic measure of maximal entropy with explicit bounds on the Lyapunov exponents. In particular, the result is true for polynomial maps hence for the homogeneous extension of to . This provides many examples where non uniform hyperbolic dynamics is established.One of the key tools is to approximate the graph of a meromorphic...
Invariant inner product in spaces of holomorphic functions on bounded symmetric domains.
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 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 the removable singularities for meromorphic mappings.
If E is a closed subset of locally finite Hausdorff (2n-2)-measure on an n-dimensional complex manifold Ω and all the points of E are nonremovable for a meromorphic mapping of Ω E into a compact Kähler manifold, then E is a pure (n-1)-dimensional complex analytic subset of Ω.
Points périodiques d’applications birationnelles de
Nous donnons une condition suffisante pour l’existence de points périodiques pour une application birationnelle de . Sous cette hypothèse, une estimation précise du nombre de points périodiques de période fixée est obtenue. Nous donnons une application de ce résultat à l’étude dynamique de ces applications, en calculant explicitement l’auto-intersection de leur courant invariant naturellement associé. Nos résultats reposent essentiellement sur le théorème de Bézout donnant le cardinal de l’intersection...
Regularization of currents and entropy
The Fujiki class and positive degree maps
We show that a map between complex-analytic manifolds, at least one ofwhich is in the Fujiki class, is a biholomorphism under a natural condition on the second cohomologies. We use this to establish that, with mild restrictions, a certain relation of “domination” introduced by Gromov is in fact a partial order.
The Hartogs-type extension theorem for meromorphic mappings into -complete complex spaces
Si dimostra un risultato di prolungamento per applicazioni meromorfe a valori in uno spazio -completo che generalizza direttamente il risultato classico di Hartogs e migliora risultati di K. Stein.
The theorem of Forelli for holomorphic mappings into complex spaces
Generalizations of the theorem of Forelli to holomorphic mappings into complex spaces are given.
Uniqueness problem for meromorphic mappings with Fermat moving hypersurfaces
We give unicity theorems for meromorphic mappings of into ℂPⁿ with Fermat moving hypersurfaces.
Uniqueness problem for meromorphic mappings with truncated multiplicities and few targets
In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of into with truncated multiplicities and “few" targets. We also give a theorem of linear degeneration for such maps with truncated multiplicities and moving targets.
Uniqueness problem of meromorphic mappings with few targets
In this paper, using techniques of value distribution theory, we give some uniqueness theorems for meromorphic mappings of Cm into CPn.
Universal reparametrization of a family of cycles : a new approach to meromorphic equivalence relations
We study analytic families of non-compact cycles, and prove there exists an analytic space of finite dimension, which gives a universal reparametrization of such a family, under some assumptions of regularity. Then we prove an analogous statement for meromorphic families of non-compact cycles. That is a new approach to Grauert’s results about meromorphic equivalence relations.
Valeurs algébriques d'une application méromorphe
Weak normal and quasinormal families of holomorphic curves
In this paper we introduce the notion of weak normal and quasinormal families of holomorphic curves from a domain in into projective spaces. We will prove some criteria for the weak normality and quasinormality of at most a certain order for such families of holomorphic curves.