Shcherbina's Theorem for Finely Holomorphic Functions

Details Shcherbina's Theorem for Finely Holomorphic Functions Shcherbina's Theorem for Finely Holomorphic Functions

2008-10-27

arxiv.org/abs/0810.4878v1

Mathematics

Complex Variables

6 pages

Scientific paper

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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