Domains with Hyperbolic Orbit Accumulation Boundary Points |
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Authors: | Sung-Yeon Kim |
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Institution: | 1.Department of Mathematics Education,Kangwon National University,Kangwon-do,Korea |
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Abstract: | Let Ω be a smoothly bounded pseudoconvex domain in ℂ
n
satisfying the condition R. Suppose that its Bergman kernel extends to `(W)]×`(W)]\overline{\Omega}\times\overline{\Omega} minus the boundary diagonal set as a locally bounded function. In this paper we show that for each hyperbolic orbit accumulation
boundary point p, there exists a contraction f∈Aut(Ω) at p. As an application, we show that Ω admits a hyperbolic orbit accumulation boundary point if and only if it is biholomorphically
equivalent to a domain defined by a weighted homogeneous polynomial and that Ω is of finite D’Angelo type. |
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Keywords: | |
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