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PERTURBATION OF DOMAINS AND AUTOMORPHISM GROUPS
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 Title & Authors
PERTURBATION OF DOMAINS AND AUTOMORPHISM GROUPS
Fridman, Buma L.; Ma, Daowei;
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 Abstract
The paper is devoted to the description of changes of the structure of the holomorphic automorphism group of a bounded domain in under small perturbation of this domain in the Hausdorff metric. We consider a number of examples when an arbitrary small perturbation can lead to a domain with a larger group, present theorems concerning upper semicontinuity property of some invariants of automorphism groups. We also prove that the dimension of an abelian subgroup of the automorphism group of a bounded domain in does not exceed n.
 Keywords
automorphism groups;perturbation of domains;Hausdorff distance;abelian subgroups;
 Language
English
 Cited by
1.
The automorphism groups of domains in complex space: a survey, Quaestiones Mathematicae, 2013, 36, 2, 225  crossref(new windwow)
2.
Model domains in ℂ3with abelian automorphism group, Complex Variables and Elliptic Equations, 2014, 59, 3, 369  crossref(new windwow)
 References
1.
E. Bedford and J. Dadok, Bounded domains with prescribed group of automor-phisms, Comment. Math. Helv. 62 (1987), 561–572 crossref(new window)

2.
G. Bredon, Introduction to compact transformation groups, Academic Press, New York, 1972

3.
D. Ebin, The manifold of Riemannian metrics, Global analysis, Proceedings of Symposium in Pure Mathematics, XV, AMS (1970), 17–40.

4.
B. L. Fridman and E. A. Poletsky, Upper semicontinuity of automorphism groups, Math. Ann. 299 (1994), 615–628. crossref(new window)

5.
B. L. Fridman, D. Ma and E. A. Poletsky, Upper semicontinuity of the dimensions of automorphism groups in $C^n$, to appear in Amer. J. Math 125 (2003)

6.
B. L. Fridman, Biholomorphic invariants of a hyperbolic manifold and some applications, Trans. Amer. Math. Soc. 276 (1983), no. 2, 685–698. crossref(new window)

7.
B. L. Fridman, A universal exhausting domain, Proc. Amer. Math. Soc. 98 (1986), 267–270. crossref(new window)

8.
B. L. Fridman, K. T. Kim, S. G. Krantz and D. Ma, On fixed points and determin-ing sets for holomorphic automorphisms, Michigan Math. J. 50 (2002), 507–515. crossref(new window)

9.
R. Greene and S. G. Krantz, The Automorphism groups of strongly pseudoconvex domains, Math. Ann. 261 (1982), 425–446. crossref(new window)

10.
R. Greene and S. G. Krantz, Stability of the Caratheodory and Kobayashi metrics and applications to biholomorphic mappings, Proceedings of Symposia in Pure Math. Providence: AMS 41 (1984), 77–94.

11.
R. Greene and S. G. Krantz, Normal Families and the Semicontinuity of Isometry and Automorphism Groups, Math. Z. 190 (1985), 455–467. crossref(new window)

12.
K. Grove and H. Karcher, How to conjugate $C^1$-close group actions, Math. Z. 132 (1973), 11–20. crossref(new window)

13.
Sh. Kobayashi, Hyperbolic Complex Spaces, Springer-Verlag, 1998

14.
D. Ma, Upper semicontinuity of isotropy and automorphism groups, Math. Ann. 292 (1992), 533–545. crossref(new window)

15.
D. Montgomery, L. Zippin, Topological transformation groups, Interscience, New York, 1955

16.
R. Palais, Equivalence of nearby differentiable actions of a group, Bull. Amer. Math. Soc. 67 (1961), 362–364 crossref(new window)

17.
E. Peschl and M. Lehtinen, A conformal self-map which fixes 3 points is the identity, Ann. Acad. Sci. Fenn., Ser. A I Math. 4 (1979), no. 1, 85–86.

18.
R. Saerens and W. R. Zame, The isometry groups of manifolds and the automor-phism groups of domains, Trans. Amer. Math. Soc. 301 (1987), 413–429 crossref(new window)

19.
A. E. Tumanov and G. B. Shabat, Realization of linear Lie groups by biholomor-phic automorphisms of bounded domains, Funct. Anal. Appl. (1990), 255–257. crossref(new window)