[Sur les domaines h-extensibles et les modèles associés]
Un point frontière d'un domaine pseudo-convexe lisse de est dit h-extensible si son multi-type de Catlin coïncide avec son multi-type de D'Angelo. Le multi-poids de Catlin définit un modèle local. Nous montrons ici qu'un domaine de avec un groupe d'automorphismes non compact est bi-holomorphiquement équivalent à son modèle associé s'il existe une suite d'automorphismes du domaine ayant une orbite convergeant non tangentiellement dans un cône, vers un point frontière h-extensible.
A boundary point of a smooth pseudoconvexdomain in is said to be h-extendible if its Catlin's multi-type coincides with its D'Angelo's multi-type. There is a local model defined by Catlin's multi-weight. In this paper, we show that a domain in with a noncompact automorphism group is biholomorphically equivalent to its associated model if there exists a sequence of automorphisms of the domain that has an orbit converging to an h-extendible boundary point non-tangentially in a cone region.
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@article{CRMATH_2016__354_9_901_0,
author = {Feng Rong and Ben Zhang},
title = {On \protect\emph{h}-extendible domains and associated models},
journal = {Comptes Rendus. Math\'ematique},
pages = {901--906},
publisher = {Elsevier},
volume = {354},
number = {9},
year = {2016},
doi = {10.1016/j.crma.2016.07.005},
language = {en},
}
Feng Rong; Ben Zhang. On h-extendible domains and associated models. Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 901-906. doi : 10.1016/j.crma.2016.07.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.07.005/
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☆ The authors are partially supported by the National Natural Science Foundation of China (Grant No. 11371246).
Commentaires - Politique
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