Convergence of formal CR mappings into strongly pseudoconvex Cauchy-Riemann manifolds

• 成果类型: Article
• 署名作者: Lamel, Bernhard; Mir, Nordine
• 署名单位: University of Vienna; Qatar Foundation (QF); Texas A&M University Qatar
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0743-3
• 发表日期: 2017
• 页码: 963-985
• 关键词: real-analytic hypersurfaces; holomorphic mappings; different dimensions; complex-spaces; MAPS; hyperquadrics; submanifolds; codimension; signature

摘要

It is shown that any formal holomorphic mapping sending a real-analytic generic submanifold M subset of C-N of finite type into a real-analytic strongly pseudoconvex CR submanifold M' subset of C-N' is necessarily convergent. As a consequence, we obtain a positive answer to the long-standing open question of whether formal holomorphic maps sending real-analytic strongly pseudoconvex hypersurfaces into each other are convergent.