Shcherbina's Theorem for Finely Holomorphic Functions
Complex Variables
2008-10-28 v1
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.
Cite
@article{arxiv.0810.4878,
title = {Shcherbina's Theorem for Finely Holomorphic Functions},
author = {Armen Edigarian and Jan Wiegerinck},
journal= {arXiv preprint arXiv:0810.4878},
year = {2008}
}
Comments
6 pages