Proper mappings between indefinite hyperbolic spaces and type I classical domains
Proper mappings between indefinite hyperbolic spaces and type I classical domains
复制标题
不定双曲空间与 I 型经典域之间的正确映射
DOI：
10.1090/tran/8618
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发表时间：
2022
影响因子：
1.3
通讯作者：
Xiao, Ming
中科院分区：
文献类型：
--
作者：
Huang, Xiaojun;Lu, Jin;Tang, Xiaomin;Xiao, Ming
在本文中，我们首先利用作者之前建立的工作来研究不定双曲空间之间的映射问题。特别是，我们概括了Baouendi-Ebenfelt-Huang [Amer. J.马斯。 133 (2011)，第 1633–1661 页] 和 Ng [密歇根数学。 J. 62 (2013)，第 769–777 页；国际。数学。资源。不是。 IMRN 2 (2015)，第 291–324 页]。然后我们使用这些结果来证明 I 型经典域之间正确的全纯映射的刚性结果，这证实了 Chan [Int.数学。资源。不，多伊。 org/10.1093/imrn/rnaa373] 在 Zaitsev-Kim [数学。安. 362 (2015)，第 639-677 页]，Kim [有界对称域之间的正确全纯映射，Springer，东京，2015 年，第 207-219 页] 和他自己。参考
In this paper, we first study a mapping problem between indefinite hyperbolic spaces by employing the work established earlier by the authors. In particular, we generalize certain theorems proved by Baouendi-Ebenfelt-Huang [Amer. J. Math. 133 (2011), pp. 1633–1661] and Ng [Michigan Math. J. 62 (2013), pp. 769–777; Int. Math. Res. Not. IMRN 2 (2015), pp. 291–324]. Then we use these results to prove a rigidity result for proper holomorphic mappings between type I classical domains, which confirms a conjecture formulated by Chan [Int. Math. Res. Not., doi. org/10.1093/imrn/rnaa373] after the work of Zaitsev-Kim [Math. Ann. 362 (2015), pp. 639-677], Kim [Proper holomorphic maps between bounded symmetric domains, Springer, Tokyo, 2015, pp. 207–219] and himself. References