Comptes Rendus
Analyse complexe, Géométrie analytique
On the boundedness of invariant hyperbolic domains
[Sur le caractère borné des domaines hyperboliques invariants]
Comptes Rendus. Mathématique, Volume 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.

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Accepté le :
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DOI : 10.5802/crmath.42
Classification : 32M05, 32T99, 32A07

Jiafu Ning 1 ; Xiangyu Zhou 2

1 Department of Mathematics, Central South University, Changsha, Hunan 410083, China.
2 Institute of Mathematics, Academy of Mathematics and Systems Science, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Jiafu Ning; Xiangyu Zhou. On the boundedness of invariant hyperbolic domains. Comptes Rendus. Mathématique, Volume 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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