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Bounds for invariant distances on pseudoconvex Levi corank one domains and applications
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 24 (2015) no. 2, pp. 281-388.

Soit D un domaine borné, lisse, de n , de fonction définissante r. Nous supposons D de corang de Levi 1, c’est-à-dire tel que la forme de Levi ¯r possède au moins (n-2) valeurs propres strictement positives en tout point du bord D de D. Le but principal de l’article est d’obtenir des estimées des distances de Caratheodory, Kobayashhi et Bergman, entre deux points quelconques de D, dépendant de la distance de ces points à la frontière ainsi que de paramètres reflétant la géométrie de Levi de D. Comme applications, nous présentons certaines propriétés de l’invariant de Fridman pour la métrique de Kobayashi sur les domaines de corang de Levi 1, nous décrivons les boules pour la métrique de Kobayashi, centrées en des points proches de la frontière, en termes de données euclidiennes, et nous étudions le comportement au bord des isométries pour la métrique de Kobayashi sur de tels domaines.

Let D n be a smoothly bounded pseudoconvex Levi corank one domain with defining function r, i.e., the Levi form ¯r of the boundary D has at least (n-2) positive eigenvalues everywhere on D. The main goal of this article is to obtain bounds for the Carathéodory, Kobayashi and the Bergman distance between a given pair of points p,qD in terms of parameters that reflect the Levi geometry of D and the distance of these points to the boundary. Applications include an understanding of Fridman’s invariant for the Kobayashi metric on Levi corank one domains, a description of the balls in the Kobayashi metric on such domains that are centered at points close to the boundary in terms of Euclidean data and the boundary behaviour of Kobayashi isometries from such domains.

Reçu le : 2014-07-06
Accepté le : 2015-02-08
Publié le : 2015-05-26
DOI : https://doi.org/10.5802/afst.1449
@article{AFST_2015_6_24_2_281_0,
     author = {G. P. Balakumar and Prachi Mahajan and Kaushal Verma},
     title = {Bounds for invariant distances on pseudoconvex Levi corank one domains and applications},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 24},
     number = {2},
     year = {2015},
     pages = {281-388},
     doi = {10.5802/afst.1449},
     mrnumber = {3358614},
     language = {en},
     url = {afst.centre-mersenne.org/item/AFST_2015_6_24_2_281_0/}
}
G. P. Balakumar; Prachi Mahajan; Kaushal Verma. Bounds for invariant distances on pseudoconvex Levi corank one domains and applications. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 24 (2015) no. 2, pp. 281-388. doi : 10.5802/afst.1449. https://afst.centre-mersenne.org/item/AFST_2015_6_24_2_281_0/

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