论文信息 - Characterization of the Hilbert ball by its Automorphisms

Characterization of the Hilbert ball by its Automorphisms

. We show in this paper that every domain in a separable Hilbert space, say H , which has a C 2 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 [KIK] and subsequent improvement of Byun/Gaussier/Kim [BGK] in the inﬁnite dimensions.

D. Ma | Kang-Tae Kim

[1] S. Krantz,et al. A Note on the Wong-Rosay Theorem in Complex Manifolds , 2002 .

[2] Kang-Tae Kim,et al. Weak-type normal families of holomorphic mappings in Banach spaces and characterization of the Hilbert ball by its automorphism group , 2001, math/0106015.

[3] Kang-Tae Kim,et al. Normal analytic polyhedra in ℂ2 with a noncompact automorphism group , 2001 .

[4] D. Ma,et al. On rigidity of Grauert tubes over locally symmetric spaces , 2000 .

[5] Seán Dineen,et al. Complex Analysis on Infinite Dimensional Spaces , 1999 .

[6] F. Berteloot. CHARACTERIZATION OF MODELS IN C2 BY THEIR AUTOMORPHISM GROUPS , 1994 .

[7] Kang-Tae Kim. Domains in Cn with a piecewise Levi flat boundary which possess a noncompact automorphism group , 1992 .

[8] S. Pinchuk,et al. Domains in Cn+1 with noncompact automorphism group , 1991 .

[9] Sidney Frankel. Complex geometry of convex domains that cover varieties , 1989 .

[10] B. Wong. Characterization of the unit ball in ℂn by its automorphism group , 1977 .

[11] R. Krantz. TAUTNESS AND COMPLETE HYPERBOLICITY OF DOMAINS IN C , 1998 .

[12] Jorge Mujica,et al. Complex analysis in Banach spaces , 1986 .