Let V be a complex variety in a bounded domain $D\subset {\mathbb{C}}^n$. We study the domain of definition for the Monge-Ampère operator of plurisubharmonic functions on V. We are also concerned with the existence and uniqueness of the Monge-Ampère equation on certain class of plurisubharmonic functions.

中文翻译：

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有界域中复变体的多次谐波函数和 Monge-Ampère 算子 ${\mathbb{C}}^n$

设V是有界域中的复变体$D\subset {\mathbb{C}}^n$. 我们研究了V上多次谐波函数的 Monge-Ampère 算子的定义域。我们还关心 Monge-Ampère 方程在某些类多次谐波函数上的存在性和唯一性。