Analytic continuation of holomorphic correspondences and equivalence of domains in Cn

• 成果类型: Article
• 署名作者: Shafikov, R
• 署名单位: State University of New York (SUNY) System; Stony Brook University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-002-0282-3
• 发表日期: 2003
• 页码: 665-682
• 关键词: pseudoconvex domains; mappings; REGULARITY; hypersurfaces; MAPS; ball

摘要

The following result is proved: Let D and D' be bounded domains in C-n, partial derivativeD is smooth, real-analytic, simply connected, and partial derivativeD' is connected, smooth, real-algebraic. Then there exists a proper holomorphic correspondence f : D --> D' if and only if there exist points p is an element of partial derivativeD and p' is an element of partial derivativeD', such that partial derivativeD and partial derivativeD' are locally CR-equivalent near p and p'. This leads to a characterization of the equivalence relationship between bounded domains in C-n modulo proper holomorphic correspondences in terms of local CR-equivalence of their boundaries.