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Dans cet article, je montre qu’un domaine est hyperbolique pour la pseudodistance intégrée de Carathéodory (c’est-à-dire que est une distance sur ) si et seulement si la pseudodistance de Carathéodory vérifie la propriété de séparation faible suivante : tout point de possède un voisinage tel que, pour tout point de , , . Je construis aussi un exemple d’un domaine -hyperbolique et non -hyperbolique.
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.
In this Note, I study existence and unicity of holomorphic retractions on complex submanifolds of dimension 1.
In this article, estimates of the hyperbolic and Carathéodory distances in domains , n ≥ 1, are obtained. They are equally valid for the Kobayashi distance.
It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with -smooth boundary. On the other hand, it is proved that the weak converse to the Suita conjecture holds for any finitely connected planar domain.
In this Note, I prove that, in many cases, the injective Kobayashi pseudodistance, as defined by Hahn, is equal to the Kobayashi pseudodistance.
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