Title

Hartogs Phenomenon on Unbounded Domains—conjectures and Examples

Abstract

In this paper we consider the Hartogs type extension problem for unbounded domains omega in C^2. The conjecture is that if the closure omega-bar does not contain any closed pseudoconcave subset K of C^2, then any function that satisfies the tangential Cauchy-Riemann equations on the boundary b-Omega can be holomorphically extended to omega. The conjecture is proved for Reinhardt tube-like domains and several related examples are given.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Hartogs extensions; CR functions; holomorphic functions

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2012 American Mathematical Society, All rights reserved.

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