## Proper mappings between indefinite hyperbolic spaces and type I classical domains

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- by Xiaojun Huang, Jin Lu, Xiaomin Tang and Ming Xiao PDF
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**375**(2022), 8465-8481 Request permission

## Abstract:

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.

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## Additional Information

**Xiaojun Huang**- Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
- MR Author ID: 333630
- Email: huangx@math.rutgers.edu
**Jin Lu**- Affiliation: Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, People’s Republic of China; and School of Internet, Anhui University, Hefei, Anhui, 230039, PEople’s Republic of China
- Email: lujin@mail.ustc.edu.cn
**Xiaomin Tang**- Affiliation: Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, People’s Republic of China
- MR Author ID: 767164
- Email: txm@zjhu.edu.cn
**Ming Xiao**- Affiliation: Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093
- Email: m3xiao@ucsd.edu
- Received by editor(s): March 27, 2021
- Received by editor(s) in revised form: November 26, 2021
- Published electronically: September 28, 2022
- Additional Notes: The first author was supported in part by NSF grants DMS-1665412 and DMS-2000050. The second author was supported in part by NSF of Zhejiang (Grant No.LY20A010007) and NNSF of China (Grant No.11801172). The third author was supported in part by NNSF of China (Grant No. 12071130, 11971165). The fourth author was supported in part by NSF grants DMS-1800549 and DMS-2045104
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**375**(2022), 8465-8481 - MSC (2020): Primary 32H35, 32M15
- DOI: https://doi.org/10.1090/tran/8618