On the automorphism group of the Kohn-Nirenberg domain. (English) Zbl 1005.32016
The Kohn-Nirenberg domain \(\operatorname{Re} w +|zw|^2 +|z|^8 + (15/7) \operatorname{Re} |z|^2 z^6 <0\) was introduced by J. J. Kohn and L. Nirenberg [Math. Ann. 201, 265–268 (1973; Zbl 0248.32013)]. The purpose of the present paper is to prove that there are no automorphism orbits of this domain that accumulate at the origin.
Reviewer: Bruce Gilligan (Regina)
MSC:
| 32M05 | Complex Lie groups, group actions on complex spaces |
| 32T99 | Pseudoconvex domains |
| 32H02 | Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables |
Citations:
Zbl 0248.32013References:
| [1] | Bedford, E.; Fornaess, J. E., A construction of peak functions on weakly pseudoconvex domains, Ann. of Math., 107, 555-568 (1978) · Zbl 0392.32004 |
| [2] | Bedford, E.; Pinchuk, S., Domains in \(C^2\) with non compact holomorphic automorphism group, Math. USSR Sbornik, 63, 141-151 (1989) · Zbl 0668.32029 |
| [3] | Bedford, E.; Pinchuk, S., Domain in \(C^{n+1}\) with non compact automorphism group, J. Geom. Anal., 1, 165-191 (1991) · Zbl 0733.32014 |
| [4] | Bell, S., Local regularity of C. R. homeomorphisms, Duke Math. J., 57, 295-300 (1988) · Zbl 0667.32017 |
| [5] | Berteloot, F., Characterization of models in \(C^2\) by their automorphism groups, Internat. J. Math., 5, 619-634 (1994) · Zbl 0817.32010 |
| [6] | Berteloot, F., A remark on local continuous extension of proper holomorphic mappings, Contemp. Math., 137, 79-83 (1992) · Zbl 0781.32027 |
| [7] | Bloom, T.; Graham, I., A geometric characterization of points of type \(m\) on real submanifolds of \(C^n\), J. Differ. Geom., 12, 171-182 (1977) · Zbl 0363.32013 |
| [8] | Catlin, D. W., Estimates of invariant metrics on pseudoconvex domains of dimension two, Math. Z., 200, 429-466 (1989) · Zbl 0661.32030 |
| [9] | D’Angelo, J. P., Real hypersurfaces, orders of contant, and applications, Ann. of Math., 115, 615-673 (1982) · Zbl 0488.32008 |
| [10] | Greene, R. E.; Krantz, S., Biholomorphic self maps of domains, Lecture Notes in Math., 1276, 136-207 (1987) · Zbl 0625.32024 |
| [11] | Kim, K. T., On a boundary point repelling automorphism orbits, J. Math. Anal. Appl., 179, 463-482 (1993) · Zbl 0816.32015 |
| [12] | K. T. Kim, and, S. Krantz, Complex scaling and domains with non-compact automorphism group, Illinois J. Math, to appear.; K. T. Kim, and, S. Krantz, Complex scaling and domains with non-compact automorphism group, Illinois J. Math, to appear. · Zbl 1065.32014 |
| [13] | Kobayashi, S., Hyperbolic Complex Spaces (1998), Springer-Verlag: Springer-Verlag Berlin/New York · Zbl 0917.32019 |
| [14] | Kohn, J. J.; Nirenberg, L., A pseudoconvex domain not admitting a holomorphic support function, Math. Ann., 201, 265-268 (1973) · Zbl 0248.32013 |
| [15] | Oeljeklaus, K., On the automorphism group of certain hyperbolic domains in \(C2\), Asterisque, 217, 193-216 (1993) · Zbl 0792.32019 |
| [16] | Rosay, J. P., Sur une characterization de la boule parmi les domains de \(C^2\) par son groupe d’automorphismes, Ann. Inst. Four. (Grenoble), 29, 91-97 (1979) · Zbl 0402.32001 |
| [17] | Wong, B., Characterization of the unit ball in \(C^n\) by its automorphism group, Invent. Math., 41, 253-257 (1977) · Zbl 0385.32016 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
