[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 = {Rong, Feng and Zhang, Ben},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.07.005/}
}
TY - JOUR AU - Rong, Feng AU - Zhang, Ben TI - On h-extendible domains and associated models JO - Comptes Rendus. Mathématique PY - 2016 SP - 901 EP - 906 VL - 354 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.07.005/ DO - 10.1016/j.crma.2016.07.005 LA - en ID - CRMATH_2016__354_9_901_0 ER -
Rong, Feng; Zhang, Ben. On h-extendible domains and associated models. Comptes Rendus. Mathématique, Tome 354 (2016) no. 9, pp. 901-906. doi : 10.1016/j.crma.2016.07.005. http://www.numdam.org/articles/10.1016/j.crma.2016.07.005/
[1] Convex domains with noncompact groups of automorphisms, Mat. Sb., Volume 185 (1994) no. 5, pp. 3-26
[2] Boundary invariants of pseudoconvex domains, Ann. of Math. (2), Volume 120 (1984) no. 3, pp. 529-586
[3] Several Complex Variables and the Geometry of Real Hypersurfaces, Stud. Adv. Math., CRC Press, Boca Raton, FL, USA, 1993
[4] Pseudoconvex domains of semiregular type, Contributions to Complex Analysis and Analytic Geometry, Asp. Math., E, vol. 26, Vieweg, Braunschweig, 1994, pp. 127-161
[5] Characterization of convex domains with noncompact automorphism group, Mich. Math. J., Volume 44 (1997) no. 2, pp. 375-388
[6] Tautness and complete hyperbolicity of domains in , Proc. Amer. Math. Soc., Volume 127 (1999) no. 1, pp. 105-116
[7] The Geometry of Complex Domains, Prog. Math., vol. 291, Birkhäuser Boston, Inc., Boston, MA, USA, 2011
[8] Complete localization of domains with noncompact automorphism groups, Trans. Amer. Math. Soc., Volume 319 (1990) no. 1, pp. 139-153
[9] Function Theory of Several Complex Variables, Pure Appl. Math., John Wiley & Sons, Inc., New York, 1982
[10] On boundary accumulation points of a convex domain in , Methods Appl. Anal., Volume 21 (2014) no. 4, pp. 427-440
[11] Biholomorphy of the model domains at a semiregular boundary point, C. R. Acad. Bulgare Sci., Volume 55 (2002) no. 5, pp. 5-8
[12] Sur une caractérisation de la boule parmi les domaines de par son groupe d'automorphismes, Ann. Inst. Fourier (Grenoble), Volume 29 (1979) no. 4, pp. 91-97 (ix)
[13] Characterization of the unit ball in by its automorphism group, Invent. Math., Volume 41 (1977) no. 3, pp. 253-257
[14] Geometric analysis on weakly pseudoconvex domains, Washington University in St. Louis, ProQuest LLC, Ann Arbor, MI, 1993 (Ph.D. thesis)
[15] Weighted boundary limits of the generalized Kobayashi–Royden metrics on weakly pseudoconvex domains, Trans. Amer. Math. Soc., Volume 347 (1995) no. 2, pp. 587-614
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☆ The authors are partially supported by the National Natural Science Foundation of China (Grant No. 11371246).
