论文标题
具有参数的适当全体形态嵌入和卡尔曼型定理的家族
Families of Proper Holomorphic Embeddings and Carleman-type Theorems with parameters
论文作者
论文摘要
我们解决了同时嵌入全体形式中的问题中的问题$ξ\ colon \ bigcup_r \ {r \} \timesΩ_r\ to \ bbb c^2 $，使得$ξ（r，\ cdot）\colonΩ_r\ knookrightArrow \ bbbb c^2 $是每个$ r $的适当的holomorphic嵌入。为此，制定并证明了Andersén-Lempert过程和Carleman定理的参数版本。
We solve the problem of simultaneously embedding properly holomorphically into $\Bbb C^2$ a whole family of $n$-connected domains $Ω_r\subset\Bbb P^1$ such that none of the components of $\Bbb P^1\setminusΩ_r$ reduces to a point, by constructing a continuous mapping $Ξ\colon\bigcup_r\{r\}\timesΩ_r\to\Bbb C^2$ such that $Ξ(r,\cdot)\colonΩ_r\hookrightarrow\Bbb C^2$ is a proper holomorphic embedding for every $r$. To this aim, a parametric version of both the Andersén-Lempert procedure and Carleman's Theorem is formulated and proved.
