Sur les domaines hyperboliques pour la distance intégrée de Carathéodory
Annales de l'Institut Fourier, Volume 46 (1996) no. 3, p. 743-753

In this paper, I prove that a domain D is hyperbolic for the Carathéodory integrated pseudodistance c D i (this means that c D i is a distance on D) if and only if the Carathéodory pseudodistance c D satisfies the following weak separation condition: for every xD, there exists a neighborhood V of x such that, yV, yx, c D (x,y)0. I also give an example of a domain D, c D i -hyperbolic but not c D -hyperbolic.

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, yx, c D (x,y))0. Je construis aussi un exemple d’un domaine c D i -hyperbolique et non c D -hyperbolique.

@article{AIF_1996__46_3_743_0,
     author = {Vigu\'e, Jean-Pierre},
     title = {Sur les domaines hyperboliques pour la distance int\'egr\'ee de Carath\'eodory},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {46},
     number = {3},
     year = {1996},
     pages = {743-753},
     doi = {10.5802/aif.1530},
     zbl = {0854.32010},
     mrnumber = {97f:32031},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1996__46_3_743_0}
}
Vigué, Jean-Pierre. Sur les domaines hyperboliques pour la distance intégrée de Carathéodory. Annales de l'Institut Fourier, Volume 46 (1996) no. 3, pp. 743-753. doi : 10.5802/aif.1530. http://www.numdam.org/item/AIF_1996__46_3_743_0/

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