### Der Kontinuitätssatz für reindimensionale &-affinoide Räume.

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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.

Let $f$ be a dominant rational map of ${\mathbb{P}}^{k}$ such that there exists $s\<k$ with ${\lambda}_{s}\left(f\right)\>{\lambda}_{l}\left(f\right)$ for all $l$. Under mild hypotheses, we show that, for $A$ outside a pluripolar set of $\mathrm{Aut}\left({\mathbb{P}}^{k}\right)$, the map $f\circ A$ admits a hyperbolic measure of maximal entropy $log{\lambda}_{s}\left(f\right)$ with explicit bounds on the Lyapunov exponents. In particular, the result is true for polynomial maps hence for the homogeneous extension of $f$ to ${\mathbb{P}}^{k+1}$. This provides many examples where non uniform hyperbolic dynamics is established.One of the key tools is to approximate the graph of a meromorphic...

We prove some normality criteria for families of meromorphic mappings of a domain $D\subset {\u2102}^{m}$ into ℂPⁿ under a condition on the inverse images of moving hypersurfaces.

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.

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.

Nous donnons une condition suffisante pour l’existence de points périodiques pour une application birationnelle de $\u2102{\mathbb{P}}^{2}$. 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...

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.

Si dimostra un risultato di prolungamento per applicazioni meromorfe a valori in uno spazio $q$-completo che generalizza direttamente il risultato classico di Hartogs e migliora risultati di K. Stein.

Generalizations of the theorem of Forelli to holomorphic mappings into complex spaces are given.

We give unicity theorems for meromorphic mappings of ${\u2102}^{m}$ into ℂPⁿ with Fermat moving hypersurfaces.

In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of ${\u2102}^{m}$ into $\u2102{P}^{n}$ with truncated multiplicities and “few" targets. We also give a theorem of linear degeneration for such maps with truncated multiplicities and moving targets.

In this paper, using techniques of value distribution theory, we give some uniqueness theorems for meromorphic mappings of Cm into CPn.

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.

In this paper we introduce the notion of weak normal and quasinormal families of holomorphic curves from a domain in $\u2102$ 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.