Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
parabolic boundary point; convex domain; automorphism group
parabolic boundary point; convex domain; automorphism group
Summary:
We prove that the one-parameter group of holomorphic automorphisms induced on a strictly geometrically bounded domain by a biholomorphism with a model domain is parabolic. This result is related to the Greene-Krantz conjecture and more generally to the classification of domains having a non compact automorphisms group. The proof relies on elementary estimates on the Kobayashi pseudo-metric.
References:
[1] Bedford, E., Pinchuk, S.: Domains in {${\mathbb C}^2$} with noncompact automorphism groups. Indiana Univ. Math. J. 47 (1998), 199-222. DOI 10.1512/iumj.1998.47.1552 | MR 1631557
[2] Bedford, E., Pinchuk, S.: Domains in {${\mathbb C}^{n+1}$} with noncompact automorphism group. J. Geom. Anal. 1 (1991), 165-191. DOI 10.1007/BF02921302 | MR 1120679
[3] Bedford, E., Pinchuk, S. I.: Domains in {${\mathbb C}^2$} with noncompact groups of holomorphic automorphisms. Math. USSR, Sb. 63 (1989), 141-151 translation from Mat. Sb., Nov. Ser. 135(177) (1988), 147-157, 271 Russian. DOI 10.1070/SM1989v063n01ABEH003264 | MR 0937803
[4] Berteloot, F.: Principe de Bloch et estimations de la métrique de Kobayashi des domaines de $\mathbb C^2$. J. Geom. Anal. 13 French (2003), 29-37. DOI 10.1007/BF02930994 | MR 1967034
[5] Berteloot, F.: Characterization of models in {$\mathbb C^2$} by their automorphism groups. Int. J. Math. 5 (1994), 619-634. DOI 10.1142/S0129167X94000322 | MR 1297410
[6] Berteloot, F., C{\oe}uré, G.: Domaines de {${\mathbb C}^2$}, pseudoconvexes et de type fini ayant un groupe non compact d'automorphismes. Ann. Inst. Fourier 41 French (1991), 77-86. DOI 10.5802/aif.1249 | MR 1112192
[7] Byun, J., Gaussier, H.: On the compactness of the automorphism group of a domain. C. R., Math., Acad. Sci. Paris 341 (2005), 545-548. DOI 10.1016/j.crma.2005.09.018 | MR 2181391 | Zbl 1086.32020
[8] Greene, R. E., Krantz, S. G.: Techniques for studying automorphisms of weakly pseudoconvex domains. Several Complex Variables: Proceedings of the Mittag-Leffler Institute, Stockholm, Sweden, 1987/1988 Math. Notes 38 Princeton University Press, Princeton (1993), 389-410 J. E. Fornæss. MR 1207869 | Zbl 0779.32017
[9] Isaev, A. V., Krantz, S. G.: Domains with non-compact automorphism group: a survey. Adv. Math. 146 (1999), 1-38. DOI 10.1006/aima.1998.1821 | MR 1706680 | Zbl 1040.32019
[10] Kang, H.: Holomorphic automorphisms of certain class of domains of infinite type. Tohoku Math. J. (2) 46 (1994), 435-442. DOI 10.2748/tmj/1178225723 | MR 1289190 | Zbl 0817.32011
[11] Kim, K.-T.: On a boundary point repelling automorphism orbits. J. Math. Anal. Appl. 179 (1993), 463-482. DOI 10.1006/jmaa.1993.1362 | MR 1249831
[12] Kim, K.-T., Krantz, S. G.: Some new results on domains in complex space with non-compact automorphism group. J. Math. Anal. Appl. 281 (2003), 417-424. DOI 10.1016/S0022-247X(03)00003-9 | MR 1982663 | Zbl 1035.32019
[13] Kim, K.-T., Krantz, S. G.: Complex scaling and domains with non-compact automorphism group. Ill. J. Math. 45 (2001), 1273-1299. DOI 10.1215/ijm/1258138066 | MR 1895457 | Zbl 1065.32014
[14] Landucci, M.: The automorphism group of domains with boundary points of infinite type. Ill. J. Math. 48 (2004), 875-885. DOI 10.1215/ijm/1258131057 | MR 2114256 | Zbl 1065.32016
[15] Rosay, J.-P.: Sur une caractérisation de la boule parmi les domaines de {${\mathbb C}^n$} par son groupe d'automorphismes. Ann. Inst. Fourier 29 French (1979), 91-97. DOI 10.5802/aif.768 | MR 0558590
[16] Wong, B.: Characterization of the unit ball in {${\mathbb C}^n$} by its automorphism group. Invent. Math. 41 (1977), 253-257. DOI 10.1007/BF01403050 | MR 0492401
Search
Partner of
