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Let a be a sequence of points in the unit ball of Cn. Eric Amar and the author have introduced the nonnegative quantity ρ(a) = infα infk Πj:j≠k dG(αj, αk), where dG is the Gleason distance in the unit disk and the first infimum is taken over all sequences α in the unit disk which map to a by a map from the disk to the ball.The value of ρ(a) is related to whether a is an interpolating sequence with respect to analytic disks passing through it, and if a is an interpolating sequence in the ball, then...

Converging semigroups of holomorphic maps

Marco Abate (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper we study the semigroups $\Phi:\mathbb{R}^{+}\rightarrow Hol(D,D)$ of holomorphic maps of a strictly convex domain $D\subset\mathbf{C}^{n}$ into itself. In particular, we characterize the semigroups converging, uniformly on compact subsets, to a holomorphic map $h:D\rightarrow\mathbf{C}^{n}$ .

Coréduction algébrique d'un espace analytique faiblement Kählérien compact.

F. Campana (1981)

Inventiones mathematicae

Correction to my Paper: Proper Holomorphic Self-Maps of the Unit Ball.

Donald Alfred Pelles (1973)

Mathematische Annalen

Correction to the paper "Distortions of a bounded domain by holomorphic mappings".

Kyong T. Hahn (1975)

Journal für die reine und angewandte Mathematik

Courants dynamiques pluripolaires

Xavier Buff (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

On montre l’existence d’applications rationnelles $f : ℙ^{k} \to ℙ^{k}$ telles que $f$ est algébriquement stable : pour tout $n \geq 0$ , $deg f^{\circ n} = {(deg f)}^{n}$ ,il existe un unique courant positif fermé $T$ de bidegré $(1, 1)$ vérifiant $f^{*} T = d \cdot T$ et $\int_{ℙ^{k}} T \land ω^{k - 1} = 1$ où $ω$ est la forme de Fubini-Study sur $ℙ^{k}$ et $T$ est pluripolaire : il existe un ensemble pluripolaire $X \subset ℙ^{k}$ tel que $\int_{X} T \land ω^{k - 1} = 1$

Courants extrémaux et dynamique complexe

Vincent Guedj (2005)

Annales scientifiques de l'École Normale Supérieure

Covering spaces of families of compact Riemann surfaces.

Terrence Napier (1992)

Mathematische Annalen

CR mappings and their holomorphic extension

Mohamed S. Baouendi, Linda P. Rothschild (1987)

Journées équations aux dérivées partielles

Cyclic Coverings: Deformation and Torelli Theorem.

Joachim Wehler (1986)

Mathematische Annalen

Das formale Prinzip für reduzierte komplexe Räume mit einer schwachen Positivitätseigenschaft.

Volker Steinbiß (1986)

Mathematische Annalen

Decay of volumes under iteration of meromorphic mappings

Vincent Guedj (2004)

Annales de l'Institut Fourier

Let $f$ be a meromorphic self-mapping of a compact Kähler manifold. We study the rate of decreasing of volumes under the iteration of $f$ . We use these volume estimates to construct the Green current of $f$ in a quite general setting.

Deformation of holomorphic maps onto Fano manifolds of second and fourth Betti numbers 1

Jun-Muk Hwang (2007)

Annales de l’institut Fourier

Let $X$ be a Fano manifold with $b_{2} = 1$ different from the projective space such that any two surfaces in $X$ have proportional fundamental classes in $H_{4} (X, C)$ . Let $f : Y \to X$ be a surjective holomorphic map from a projective variety $Y$ . We show that all deformations of $f$ with $Y$ and $X$ fixed, come from automorphisms of $X$ . The proof is obtained by studying the geometry of the integral varieties of the multi-valued foliation defined by the variety of minimal rational tangents of $X$ .

Degeneracy of entire curves in log surfaces with $\bar{q} = 2$

Jörg Winkelmann (2011)

Annales de l’institut Fourier

We determine which algebraic surface of logarithmic irregularity $2$ admit an algebraically non-degenerate entire curve.

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