Jean-Pierre Vigué

Common fixed points in hyperbolic Riemann surfaces and convex domains

In this paper we prove that a commuting family of continuous selfmaps of a bounded convex domain in Cn which are holomorphic in the interior has a common fixed point. The proof makes use of three basic ingredients: iteration theory of holomorphic maps, a precise description of the structure of the boundary of a convex domain, and a similar result for commuting families of self-maps of a hyperbolic domain of a compact Riemann surface.

Sur les ensembles d'unicité pour les automorphismes analytiques d'un domaine borné

In this Note, we study the determination sets for the group Aut(D) of holomorphic automorphisms of a bounded domain D in Cn. To cite this article: J.-P. Vigue, C. R. Acad. Sci. Paris, Ser. I 336 (2003).

Automorphismes analytiques des domaines produits

In this paper, I study the group of analytic automorphisms of a bounded product domain in the spaceC(S,C) of continuous functions on a compact spaceS. I prove that its automorphism group is a Lie group and I am able to prove which are the bounded symmetric ones.

La métrique infinitésimale de Kobayashi et la caractérisation des domaines convexes bornés

Abstract This paper deals with the characterization of a domain D in C n by the Kobayashi infinitesimal metric in a neighborhood of a point a of D. I prove this characterization in the following cases: a domain D in C analytically isomorphic to the open unit disc, an hyperbolic domain D in C , a bounded strictly convex domain D in C n and also a bounded convex domain D in C n which is isomorphic to an open unit ball. The proofs use the result of L. Lempert on the equality of the Caratheodory and Kobayashi infinitesimal metric on convex domains and the notion of complex geodesic.

An example of a Carathéodory complete but not finitely compact analytic space

An analytic space is given which is c^-complete but not Cy-finitely compact.

Un lemme de Schwarz pour les boules-unités ouvertes

RESUME. Let B1 and B2 be the open unit balls of Cn1 and Cn2 for the norms k . k1 and k . k2 . Let f : B1 ! B2 be a holomorphic mapping such that f (0) ≥ 0. It is well known that, for every z 2 B1, kf (z)k2 kzk1, and kf 0(0)k 1. In this paper, I prove the converse of this result. Let f : B1 ! B2 be a holomorphic mapping such that f 0(0) is an isometry. If B2 is strictly convex, I prove that f (0) ≥ 0 and that f is linear. I also define the rank of a point x belonging to the boundary of B1 or B2. Under some hypotheses on the ranks, I prove that a holomorphic mapping such that f (0) ≥ 0 and that f 0(0) is an isometry is linear.

La distance de Caratheodory sur un produit continu de domaines bornes

Dans ce papier, je montre pour la distance de Caratheodory sur un produit continu B de domaines (B s ) s∈S la formule: C B (f,g) = maxC Bs (f(s),g(s)). In this paper, I prove for the Caratheodory distance on a continuous product B ofdomains (B s ) s∈S the formula: C B (f,g) = max cB s (f(s),g(s)).