Shcherbina's Theorem for Finely Holomorphic Functions

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
6 pages

Keywords

Complex Variables, 32U15; 32H40; 31C40

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/172534

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0810.4878
 http://arxiv.org/abs/0810.4878

Collections

arXiv