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Vietnam Journal of Mathematics 37:2&3 (2009) 179-190 

Geometry of Domains in Cⁿ with Noncompact Automorphism Groups

Do Duc Thai and Ninh Van Thu

Abstract.  We survey results arising from the study of domains in Cⁿ with non-compact automorphism group in the past ten years. Beginning with well-known characterizations of smoothly bounded domains with non-compact automorphism group, we develop ideas toward characterizations of arbitrary (not necessary bounded) domains in Cⁿ.

2000 Mathematics Subject Classification: 32M17, 32Q45, 51M15.

Keywords: Automorphism group of a complex manifold, a domain of finite type, the scaling technique.

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