非等维Fock-Bargmann-Hartogs域间固有全纯映射的刚性

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-02-27 DOI:10.1112/blms.70038

Guicong Su, Lei Wang

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引用次数: 0

摘要

在本文中，我们引入了一个新的刚性定理来研究变维的Fock-Bargmann-Hartogs域之间的真全纯映射。与以往的研究不同，这个定理没有对余维数施加任何限制。我们的主要结果证明了任何这样的固有全纯映射F$ F$可以等价地表示为(k z 1，…，K zn, 0，…，0,w K)$ (\sqrt {K} z_1,\ldots, \sqrt {K} z_n, 0,\ldots, 0, w^ K)$，其中k$ k$是一个正整数。

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Rigidity of proper holomorphic maps between nonequidimensional Fock–Bargmann–Hartogs domains

In this article, we introduce a novel rigidity theorem that investigates proper holomorphic maps between Fock–Bargmann–Hartogs domains of varying dimensions. Unlike previous studies, this theorem does not impose any restrictions on the codimension. Our main result demonstrates that any such proper holomorphic map $F$ can be equivalently represented as $(\sqrt{k} z_{1}, …, \sqrt{k} z_{n}, 0, …, 0, w^{k})$ , where $k$ is a positive integer.