Building on work of Du, Gao, and Yau, we give a characterization of smooth solutions, up to normalization, of the complex Plateau problem for strongly pseudoconvex Calabi--Yau CR manifolds of dimension $2n-1 \ge 5$ and in the hypersurface case when $n=2$, a case that was completely solved by Yau for $n \ge 3$ but only partially solved by Du and Yau for $n=2$. As an application, we determine the existence of a link-theoretic invariant of normal isolated singularities that distinguishes smooth points from singular ones.

中文翻译：

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复杂高原问题的平滑解决方案

在 Du、Gao 和 Yau 的工作的基础上，我们给出了维数为 $2n-1 \ge 5$ 的强赝赝凸 Calabi-Yau CR 流形的复杂 Plateau 问题的平滑解直至归一化的特征，并且在$n=2$ 时的超曲面案例，Yau 完全解决了 $n \ge 3$ 的情况，但 Du 和 Yau 仅部分解决了 $n=2$ 的情况。作为一个应用程序，我们确定了正常孤立奇异点的链接理论不变量的存在，该不变量将平滑点与奇异点区分开来。