Domains with Hyperbolic Orbit Accumulation Boundary Points
Domains with Hyperbolic Orbit Accumulation Boundary Points
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具有双曲轨道累积边界点的域
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Sung
中科院分区：
文献类型：
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作者：
Sung
设Ω是ℂn中满足条件R的光滑有界伪凸域，假设它的Bergman核扩张到$OVERLINE{OMEGA}$减去边界对角线集为局部有界函数.本文证明了对于每个双曲轨道积累边界点p，在p处存在一个压缩f∈aut(Ω).作为应用，我们证明了Ω允许双曲轨道积累边界点当且仅当它与由加权齐次多项式定义的区域是双全纯等价的，并且Ω是有限D‘Angelo型的.
Let Ω be a smoothly bounded pseudoconvex domain in ℂn satisfying the condition R. Suppose that its Bergman kernel extends to $overline{Omega} imesoverline{Omega}$ 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.