Shcherbina's Theorem for Finely Holomorphic Functions

Armen Edigarian; Jan Wiegerinck

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arXiv · 0810.4878

Shcherbina's Theorem for Finely Holomorphic Functions

Armen Edigarian·Jan Wiegerinck

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Abstract

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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Armen Edigarian, Jan Wiegerinck. 2008-10-27. Shcherbina's Theorem for Finely Holomorphic Functions. https://arxiv.org/abs/0810.4878

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