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Schwarz-type lemmas for solutions of ¯ -inequalities and complete hyperbolicity of almost complex manifolds

Sergey Ivashkovich, Jean-Pierre Rosay (2004)

Annales de l'Institut Fourier

The definition of the Kobayashi-Royden pseudo-metric for almost complex manifolds is similar to its definition for complex manifolds. We study the question of completeness of some domains for this metric. In particular, we study the completeness of the complement of submanifolds of co-dimension 1 or 2. The paper includes a discussion, with proofs, of basic facts in the theory of pseudo-holomorphic discs.

Strengthened Moser’s conjecture, geometry of Grunsky coefficients and Fredholm eigenvalues

Samuel Krushkal (2007)

Open Mathematics

The Grunsky and Teichmüller norms ϰ(f) and k(f) of a holomorphic univalent function f in a finitely connected domain D ∋ ∞ with quasiconformal extension to ^ are related by ϰ(f) ≤ k(f). In 1985, Jürgen Moser conjectured that any univalent function in the disk Δ* = z: |z| > 1 can be approximated locally uniformly by functions with ϰ(f) < k(f). This conjecture has been recently proved by R. Kühnau and the author. In this paper, we prove that approximation is possible in a stronger sense, namely,...

Sur les domaines hyperboliques pour la distance intégrée de Carathéodory

Jean-Pierre Vigué (1996)

Annales de l'institut Fourier

Dans cet article, je montre qu’un domaine D est hyperbolique pour la pseudodistance intégrée de Carathéodory c D i (c’est-à-dire que c D i est une distance sur D ) si et seulement si la pseudodistance de Carathéodory c D vérifie la propriété de séparation faible suivante : tout point x de D possède un voisinage V tel que, pour tout point y de V , y x , c D ( x , y ) ) 0 . Je construis aussi un exemple d’un domaine c D i -hyperbolique et non c D -hyperbolique.

Sur les espaces complets pour la distance de Carathéodory

Larbi Belkhchicha, Jean-Pierre Vigué (1994)

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

An example of a finite dimensional analytic space is exhibited, for which the Carathéodory integrated distance and the Carathéodory distance, although defining the same topology, are respectively complete and incomplete.

Sur les rétractes holomorphes de dimension 1

Jean-Pierre Vigué (1998)

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

In this Note, I study existence and unicity of holomorphic retractions on complex submanifolds of dimension 1.

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