Hartogs Phenomenon on Unbounded Domains—conjectures and Examples
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.
A. Boggess et al., "Hartogs Phenomenon on Unbounded Domains—conjectures and Examples," CRM Proceedings and Lecture Notes, American Mathematical Society, Jan 2012.
Mathematics and Statistics
Keywords and Phrases
Hartogs extensions; CR functions; holomorphic functions
Article - Journal
© 2012 American Mathematical Society, All rights reserved.