In this article, the author discusses the dimension of holomorphic automorphism groups on hyperbolic Reirihardt domains. and classifies those hyperbolic Reinhardt domains whose automorphism group has prescribed dimens...In this article, the author discusses the dimension of holomorphic automorphism groups on hyperbolic Reirihardt domains. and classifies those hyperbolic Reinhardt domains whose automorphism group has prescribed dimension n2 - 2 (where n is the dimension of domain).展开更多
For a class of Reinhardt domains, we prove that the holomorphic sectional curvatures are upper-bounded by a negative constant. Then we obtain a comparison theorem for the Kobayashi and Bergman metrics on the domains.
Let D be a bounded positive(m, p)-circle domain in C^2. The authors prove that if dim(Iso(D)~0) = 2, then D is holomorphically equivalent to a Reinhardt domain; if dim(Iso(D)~0) = 4, then D is holomorphically equivale...Let D be a bounded positive(m, p)-circle domain in C^2. The authors prove that if dim(Iso(D)~0) = 2, then D is holomorphically equivalent to a Reinhardt domain; if dim(Iso(D)~0) = 4, then D is holomorphically equivalent to the unit ball in C^2. Moreover,the authors prove the Thullen's classification on bounded Reinhardt domains in C^2 by the Lie group technique.展开更多
In this paper, we give an explicit formula of the Bergman kernel function on Hua Construction of the second type when the parameters 1/p1,…, 1/pr-1 are positive integers and 1/pr is an arbitrary positive real number.
基金The first author's work was supported in part by the National Natural Science Foundation of China (Grant No.10571135)the Doctoral Program Foundation of the Ministry of Education of China (Grant No. 20050240711)
文摘It is proved that every proper holomorphic self-map of a smooth bounded Reinhardt domain in C^2 is an automorphism.
基金Supported by the National Natural Science Foundation of China (10501036)the Natural Science Foundation of Fujian Province of China (Z0511003).
文摘In this article, the author discusses the dimension of holomorphic automorphism groups on hyperbolic Reirihardt domains. and classifies those hyperbolic Reinhardt domains whose automorphism group has prescribed dimension n2 - 2 (where n is the dimension of domain).
基金Project supported partly by the National Natural Science Foundation of China
文摘For a class of Reinhardt domains, we prove that the holomorphic sectional curvatures are upper-bounded by a negative constant. Then we obtain a comparison theorem for the Kobayashi and Bergman metrics on the domains.
基金supported by the National Natural Science Foundation of China(Nos.11571288,11671330,11771357)
文摘Let D be a bounded positive(m, p)-circle domain in C^2. The authors prove that if dim(Iso(D)~0) = 2, then D is holomorphically equivalent to a Reinhardt domain; if dim(Iso(D)~0) = 4, then D is holomorphically equivalent to the unit ball in C^2. Moreover,the authors prove the Thullen's classification on bounded Reinhardt domains in C^2 by the Lie group technique.
文摘In this paper, we give an explicit formula of the Bergman kernel function on Hua Construction of the second type when the parameters 1/p1,…, 1/pr-1 are positive integers and 1/pr is an arbitrary positive real number.
