卡勒林地区高原问题
Probleme Plateau complexe dans les varietes Kahleriennes
摘要：
复流形X中的"复高原问题“（或边界问题）是刻画X的实子流形$Γ$的问题，这些实子流形是$X \backslash Γ$的解析子簇的边界。我们的主要结果处理$X=U\timesω$的情况，其中$U$是一个连通的复流形和$ω$是一个盘凸Kähler流形。作为结果，我们得到了Harvey-Lawson，Dolbeault-Henkin和Dinh的结果。我们给出了Hartogs-Levi定理和Hartogs-Bochner定理的推广。最后，证明了可嵌入紧致Kähler流形的严格伪凸CR结构可嵌入$\CC^n$的充要条件是它有一个非常数CR函数.
英文摘要：
The ``complex Plateau problem'' (or boundary problem) in a complexe manifold X is the problem of characterizing the real submanifolds $Γ$ of X which are boundaries of analytic sub-varieties of $X \backslash Γ$. Our principal result treat the case $X=U\timesω$ where $U$ is a connected complex manifold and $ω$ is a disk-convex Kähler manifold. As a consequence, we obtain results of Harvey-Lawson, Dolbeault-Henkin and Dinh. We give generalizations of Hartogs-Levi and Hartogs-Bochner theorems. Finally, we prove that a strictly pseudo-convex CR structure embeddable in a compact Kähler manifold is embeddable in $\CC^n$ if and only if it has a non constant CR function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
