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Comptes Rendus. Mathématique

Analyse complexe, Géométrie analytique
On the boundedness of invariant hyperbolic domains
[Sur le caractère borné des domaines hyperboliques invariants]
Comptes Rendus. Mathématique, Tome 358 (2020) no. 3, pp. 321-326.

Dans cet article, nous généralisons un théorème de A. Kodama sur le caractère borné des domaines circulaires hyperboliques. Nous démontrons que si K est un groupe de Lie compact qui agit linéairement sur n et vérifie 𝒪( n ) K =, et si Ω est un domaine K-invariant orbitalement convexe de n qui contient 0, alors Ω est borné si et seulement s’il est hyperbolique au sens de Kobayashi.

In this paper, we generalize a theorem of A. Kodama about boundedness of hyperbolic circular domains. We will prove that if K is a compact Lie group which acts linearly on n with 𝒪( n ) K =, and Ω is a K-invariant orbit convex domain in n which contains 0, then Ω is bounded if and only if Ω is Kobayashi hyperbolic.

Reçu le :
Accepté le :
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DOI : https://doi.org/10.5802/crmath.42
Classification : 32M05,  32T99,  32A07
@article{CRMATH_2020__358_3_321_0,
     author = {Jiafu Ning and Xiangyu Zhou},
     title = {On the boundedness of invariant hyperbolic domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {321--326},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {3},
     year = {2020},
     doi = {10.5802/crmath.42},
     language = {en},
}
Jiafu Ning; Xiangyu Zhou. On the boundedness of invariant hyperbolic domains. Comptes Rendus. Mathématique, Tome 358 (2020) no. 3, pp. 321-326. doi : 10.5802/crmath.42. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.42/

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