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CHARACTERIZATION OF THE HILBERT BALL BY ITS AUTOMORPHISMS
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 Title & Authors
CHARACTERIZATION OF THE HILBERT BALL BY ITS AUTOMORPHISMS
Kim, Kang-Tae; Ma, Daowei;
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 Abstract
We show in this paper that every domain in a separable Hilbert space, say H, which has a smooth strongly pseudoconvex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of H. This is the complete generalization of the Wong-Rosay theorem to a separable Hilbert space of infinite dimension. Our work here is an improvement from the preceding work of Kim/Krantz [10] and subsequent improvement of Byun/Gaussier/Kim [3] in the infinite dimensions.
 Keywords
automorphism group;Hilbert ball;weak-strong normal family;
 Language
English
 Cited by
1.
A note on Kim–Ma characterization of the Hilbert ball, Journal of Mathematical Analysis and Applications, 2005, 309, 2, 761  crossref(new windwow)
2.
Model domains in ℂ3with abelian automorphism group, Complex Variables and Elliptic Equations, 2014, 59, 3, 369  crossref(new windwow)
3.
Some Aspects of the Kobayashi and Carathéodory Metrics on Pseudoconvex Domains, Journal of Geometric Analysis, 2012, 22, 2, 491  crossref(new windwow)
4.
Characterization of the unit ball in C n among complex manifolds of dimensionn, Journal of Geometric Analysis, 2004, 14, 4, 697  crossref(new windwow)
 References
1.
E. Bedford and S. Pinchuk, Domains in $\mathbb{C}^{n+1}$ with noncompact automorphism group, J. Geom. Anal. 1 (1992), 165–191 crossref(new window)

2.
F. Berteloot, Characterization of models in $\mathbb{C}^2$ by their automorphism groups, Internat. J. Math. 5 (1994), 619–634 crossref(new window)

3.
J. Byun, H. Gaussier and K. Kim, Weak-type normal families of holomorphic mappings in Banach spaces and Characterization of the Hilbert ball by its auto-morphism group, J. Geom. Anal. 12 (2002), 581–599 crossref(new window)

4.
S. Dineen, Complex analysis on infinite dimensional spaces, Springer Monograph Ser., 1999

5.
A. Efimov, A generalization of the Wong-Rosay theorem for the unbounded case, Sb. Math. 186 (1995), 967–976 crossref(new window)

6.
S. Frankel, Complex geometry with convex domains that cover varieties, Acta Math. 163 (1989), 109–149 crossref(new window)

7.
H. Gaussier, Tautness and complete hyperbolicity of domains in $\mathbb{C}^n$, Proc. Amer. Math. Soc. 127 (1999), 105–116 crossref(new window)

8.
H. Gaussier, K. T. Kim and S. G. Krantz, A note on the Wong-Rosay theorem in complex manifolds, Complex Variables 47 (2002), 761–768 crossref(new window)

9.
K. T. Kim, Domains in $\mathbb{C}^n$ with a piecewise Levi flat boundary which possess a noncompact automorphism group, Math. Ann. 292 (1992), 575–586 crossref(new window)

10.
K. T. Kim and S. G. Krantz, Characterization of the Hilbert ball by its automor-phism group, Trans. Amer. Math. 354 (2002), 2797–2838 crossref(new window)

11.
K. T. Kim, S. G. Krantz and A. F. Spiro, Analytic polyhedra in $\mathbb{C}^n$ with a non-compact automorphism group, preprint

12.
K. T. Kim and A. Pagano, Normal analytic polyhedra in $\mathbb{C}^n$ with a non-compact automorphism group, J. Geom. Anal. 11 (2001), 283–293. crossref(new window)

13.
D. Ma and S. J. Kan, On rigidity of Grauert tubes over locally symmetric spaces, J. Reine Angew. Math. 524 (2000), 205–225. crossref(new window)

14.
J. Mujica, Complex analysis in Banach spaces, North-Holland, 1986

15.
S. Pincuk, Holomorphic inequivalence of certain classes of domains in $\mathbb{C}^n$, Mat. Sb. 111 (153) (1981), No. 1, 67–94.

16.
J. P. Rosay, Une caracterization de la boule parmi les domaines de $\mathbb{C}^n$ par son groupe d'automorphismes, Ann. Inst. Fourier (Grenoble) XXIX (1979), 91–97

17.
N. Sibony, A class of hyperbolic manifolds, Recent developments in several complex variables, Ann. Math. Studies 100 (1981), 357–372

18.
B. Wong, Characterization of the unit ball in $\mathbb{C}^n$ by its automorphism group, Invent. Math. 41 (1977), 253–257 crossref(new window)