Inverse of Abelian integrals and ramified Riemann domains

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• 作者：Junjiro Noguchi
• 关键词：Mathematics Subject Classification32E40 ; 32D26 ; 30F99
• 刊名：Mathematische Annalen
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：367
• 期：1-2
• 页码：229-249
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1807
• 卷排序：367

文摘

We deal with the Levi problem (Hartogs’ inverse problem) for ramified Riemann domains by introducing a positive scalar function \(\rho (a, X)\) for a complex manifold X with a global frame of the holomorphic cotangent bundle by closed Abelian differentials, which is an analogue of Hartogs’ radius. We obtain some geometric conditions in terms of \(\rho (a, X)\) which imply the validity of the Levi problem for finitely sheeted ramified Riemann domains over \({\mathbf {C}}^n\). On the course, we give a new proof of the Behnke–Stein Theorem.