Meromorphic extension spaces
The aim of the present paper is to study meromorphic extension spaces. The obtained results allow us to get the invariance of meromorphic extendibility under finite proper surjective holomorphic maps.
Méthodes de changement d’échelles en analyse complexe
Nous mettons en perspective différentes méthodes de changement d’échelles et illustrons leur pertinence en mettant sur pieds des preuves simples et élémentaires de plusieurs théorèmes biens connus en analyse ou géométrie complexe. Les situations abordées sont variées et la plupart des théorèmes démontrés sont des classiques initialement obtenus entre la fin du xixe et la seconde moitié du xxe siècle.
Moduli spaces of holomorphic mappings into hyperbolically imbedded complex spaces and locally symmetric spaces.
Non-Archimedean analytic curves in Abelian varieties.
Non-deformability of entire curves in projective hypersurfaces of high degree
In this article, we prove that there does not exist a family of maximal rank of entire curves in the universal family of hypersurfaces of degree in the complex projective space . This can be seen as a weak version of the Kobayashi conjecture asserting that a general projective hypersurface of high degree is hyperbolic in the sense of Kobayashi.
Normal pseudoholomorphic curves
First, we give some characterizations of J-hyperbolic points for almost complex manifolds. We apply these characterizations to show that the hyperbolic embeddedness of an almost complex submanifold follows from relative compactness of certain spaces of continuous extensions of pseudoholomorphic curves defined on the punctured unit disc. Next, we define uniformly normal families of pseudoholomorphic curves. We prove extension-convergence theorems for these families similar to those obtained by Kobayashi,...
On Brody and entire curves
We discuss an example of an open subset of a torus which admits a dense entire curve, but no dense Brody curve.
On D*-extension property of the Hartogs domains.
A complex analytic space is said to have the D*-extension property if and only if any holomorphic map from the punctured disk to the given space extends to a holomorphic map from the whole disk to the same space. A Hartogs domain H over the base X (a complex space) is a subset of X x C where all the fibers over X are disks centered at the origin, possibly of infinite radius. Denote by φ the function giving the logarithm of the reciprocal of the radius of the fibers, so that, when X is pseudoconvex,...
On isometries of the carathéodory and Kobayashi metrics on strongly pseudoconvex domains
Let and be domains in and an isometry for the Kobayashi or Carathéodory metrics. Suppose that extends as a map to . We then prove that is a CR or anti-CR diffeomorphism. It follows that and must be biholomorphic or anti-biholomorphic.
On isometries of the Kobayashi and Carathéodory metrics
This article considers C¹-smooth isometries of the Kobayashi and Carathéodory metrics on domains in ℂⁿ and the extent to which they behave like holomorphic mappings. First we provide an example which suggests that 𝔹ⁿ cannot be mapped isometrically onto a product domain. In addition, we prove several results on continuous extension of C⁰-isometries f : D₁ → D₂ to the closures under purely local assumptions on the boundaries. As an application, we show that there is no C⁰-isometry between a strongly...
On proper R-actions on hyperbolic Stein surfaces.
On the -extension and the Hartogs extension
On the Hausdorff measures associated to the Carathéodory and Kobayashi metrics
Orbifolds, special varieties and classification theory
This article gives a description, by means of functorial intrinsic fibrations, of the geometric structure (and conjecturally also of the Kobayashi pseudometric, as well as of the arithmetic in the projective case) of compact Kähler manifolds. We first define special manifolds as being the compact Kähler manifolds with no meromorphic map onto an orbifold of general type, the orbifold structure on the base being given by the divisor of multiple fibres. We next show that rationally connected Kähler...
Orbifolds, special varieties and classification theory: an appendix
For any compact Kähler manifold and for any equivalence relation generated by a symmetric binary relation with compact analytic graph in , the existence of a meromorphic quotient is known from Inv. Math. 63 (1981). We give here a simplified and detailed proof of the existence of such quotients, following the approach of that paper. These quotients are used in one of the two constructions of the core of given in the previous paper of this fascicule, as well as in many other questions.
Plane curves with hyperbolic and -hyperbolic complements
Remark on hyperbolic embeddability of relatively compact subspaces of complex spaces
Abstract. The characterization of hyperbolic embeddability of relatively compact subspaces of a complex space in terms of extension of holomorphic maps from the punctured disc and of limit complex lines is given.
Remarks on the relative intrinsic pseudo-distance and hyperbolic imbeddability
We prove the invariance of hyperbolic imbeddability under holomorphic fiber bundles with compact hyperbolic fibers. Moreover, we show an example concerning the relation between the Kobayashi relative intrinsic pseudo-distance of a holomorphic fiber bundle and the one in its base.
Rigidity of Holomorphic Self-Mappings and the Automorphism Groups of Hyperbolic Stein Spaces.
Schottky-Landau growth estimates for s-normal families of holomorphic mappings.