La pseudodistance de Caratheodory sur des ouverts emboites
Given two open sets U_1 contained in U_2, we compare the Caratheodory pseudodistance on U_1 and U_2.
math.CV↗
arXiv subjects
Jean-Pierre Vigue
Publications and source records attributed to Jean-Pierre Vigue.
Distances invariantes et points fixes d'applications holomorphes
In this paper, we prove the following result : let X be a complex manifold, hyperbolic for the Carathéodory distance and let U be an open set relatively compact in X. Then, there exists k<1 such that we get, for the Carathéodory infinitesimal metric E_X(x,v) less or equal to kE_U(x,v). We also get results concerning fixed points of holomorphic mappings from X to U.
math.CV↗
Points fixes d'applications holomorphes d'un domaine borne de C^n dans lui-meme
In this paper, we prove the main properties of the set of fixed points of an holomorphic map from a bounded domain in C^n into itself.
math.CV↗
Sur la Caracterisation des Retractes Holomorphes a l'aide de la Metrique Infinitesimale de Kobayashi
Dans cet article, on donne une caracterisation des retractes holomorphes a l'aide de la metrique infinitesimale de Kobayashi ----- This article gives a characterization of holomorphic retractions using Kobayashi's infinitesimal metric.
math.CV↗
Isometries for the Caratheodory Metric
Under certain hypothesises, we prove that a map which is an isometry for the Caratheodory infinitesimal metric at a point is an analytic isomorphism onto its image.
math.FA↗
Fixed points and Determining Sets for Holomorphic Self-Maps of a Hyperbolic Manifold
We study fixed point sets for holomorphic automorphisms (and endomorphisms) on complex manifolds. The main object of our interest is to determine the number and configuration of fixed points that forces an automorphism (endomorphism) to be the identity. These questions have been examined in a number of papers for a bounded domain in ${\Bbb C}^n$. Here we resolve the case for a general finite dimensional hyperbolic manifold. We also show that the results for non-hyperbolic manifolds are notably different.
math.CV↗
Isolated fixed point sets for holomorphic maps
We study discrete fixed point sets of holomorphic self-maps of complex manifolds. The main attention is focused on the cardinality of this set and its configuration. As a consequence of one of our observations, a bounded domain in ${\Bbb C}^n$ with no non-trivial holomorphic retractions is constructed.
math.CV↗