在强伪凸区域嵌入有边黎曼曲面

IF 0.2 Q4 MATHEMATICS

REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES Pub Date : 2022-04-14 DOI:10.59277/rrmpa.2023.83.94

F. Forstnerič

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引用次数: 1

摘要

我们证明了在Cn, n > 1中，具有光滑边界bM的每一个有边界的Riemann曲面M允许一个适当的全纯映射M→Ω进入任何有界的强伪凸域Ω，并扩展到一个光滑映射f: M→Ω，当n≥3时可以选择浸入，当n≥4时可以选择嵌入。此外，可以选择f来近似M中的紧簇上的给定全纯映射M→Ω，并将其插值到M中的有限多个给定点。

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EMBEDDING BORDERED RIEMANN SURFACES IN STRONGLY PSEUDOCONVEX DOMAINS

We show that every bordered Riemann surface, M, with smooth boundary bM admits a proper holomorphic map M → Ω into any bounded strongly pseudoconvex domain Ω in Cn, n > 1, extending to a smooth map f : M → Ω which can be chosen an immersion if n ≥ 3 and an embedding if n ≥ 4. Furthermore, f can be chosen to approximate a given holomorphic map M → Ω on compacts in M and interpolate it at finitely many given points in M.

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来源期刊

REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES MATHEMATICS-

CiteScore

0.50

自引率

0.00%

发文量