论文标题
将边界的黎曼表面嵌入强烈的假子共晶域中
Embedding bordered Riemann surfaces in strongly pseudoconvex domains
论文作者
论文摘要
我们表明，每个边界的Riemann表面（$ m $），带有光滑边界$ bm $承认适当的霍明型地图$ m \ toω$进入任何有界的强烈pseudoconvex romain $ω$中的$ \ mathbb c^n $，$ n $，$ n> 1美元3 $，如果$ n \ ge 4 $。此外，可以选择$ f $以近似给定的全态映射$ \ operline m \ to $ m $中的紧凑型$ω$，并以$ m $中的许多给定点有限地插入。
We show that every bordered Riemann surface, $M$, with smooth boundary $bM$ admits a proper holomorphic map $M\to Ω$ into any bounded strongly pseudoconvex domain $Ω$ in $\mathbb C^n$, $n>1$, extending to a smooth map $f:\overline M\to\overline Ω$ which can be chosen an immersion if $n\ge 3$ and an embedding if $n\ge 4$. Furthermore, $f$ can be chosen to approximate a given holomorphic map $\overline M\to Ω$ on compacts in $M$ and interpolate it at finitely many given points in $M$.
