精细全纯函数的Shcherbina定理
Shcherbina's Theorem for Finely Holomorphic Functions
摘要：
我们证明了一个类似的萨杜拉耶夫定理的大小的集合中的一个最大的全实流形可以满足一个pluripolar集。流形必须是C-1类的。这很容易导致一个版本的Shcherbina定理的C-1功能f的定义在一个邻域内的某些紧集K在复平面。若f在K上的图是多极图，则f在K的精细内部的闭包中满足柯西-黎曼方程。
英文摘要：
We prove an analogue of Sadullaev's theorem concerning the size of the set where a maximal totally real manifold can meet a pluripolar set. The manifold has to be of class C-1 only. This readily leads to a version of Shcherbina's theorem for C-1 functions f that are defined in a neighborhood of certain compact sets K in the complex plane. If the graph of f on K is pluripolar, then f satisfies the Cauchy Riemann equations in the closure of the fine interior of K.
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