On <i>h</i>-extendible domains and associated models

Feng Rong; Ben Zhang

doi:10.1016/j.crma.2016.07.005

Complex analysis

On h-extendible domains and associated models

Presented by: Jean-Pierre Demailly

Feng Rong ¹; Ben Zhang ¹

¹ Department of Mathematics, School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai, 200240, PR China

Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 901-906.

Abstract
Résumé

A boundary point of a smooth pseudoconvexdomain in $C^{n}$ 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 $C^{n}$ 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.

Un point frontière d'un domaine pseudo-convexe lisse de $C^{n}$ 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 $C^{n}$ 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.

Received: 2016-04-05
Accepted: 2016-07-18
Published online: 2016-07-29

DOI: 10.1016/j.crma.2016.07.005

Author's affiliations:

Feng Rong ¹; Ben Zhang ¹

¹ Department of Mathematics, School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai, 200240, PR China

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     title = {On \protect\emph{h}-extendible domains and associated models},
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     pages = {901--906},
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     year = {2016},
     doi = {10.1016/j.crma.2016.07.005},
     language = {en},
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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).

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