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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. 

Carbonium ions are an important class of reaction intermediates, but their dynamic evolution is difficult to be monitored by in situ techniques under experimental conditions because of their extremely short lifetime. Probably the most famous case is 2‐norbornyl cation (2NB⁺): its existing form (classical or non‐classical) had been debated for decades, until the concrete proof of non‐classical geometry was achieved by X‐ray crystallographic characterization at ultra‐low temperature (40 K) and super acidic environment. However, we lack the understanding about 2NB⁺at ambient conditions. Herein, by taking advantage of the confinement effect and delocalized acidic environment of zeolites, we successfully stabilized 2NB⁺and unequivocally confirmed its “non‐classical” structure inside the ZSM‐5 zeolite byab initiomolecular dynamics simulations and¹³C solid‐state nuclear magnetic resonance experiments. It is the first time to in situ observe the non‐classical 2NB⁺without the super acidic environment at ambient temperature, which provides a new strategy to expand the carbocation chemistry.

 

Carbonium ions are an important class of reaction intermediates, but their dynamic evolution is difficult to be monitored by in situ techniques under experimental conditions because of their extremely short lifetime. Probably the most famous case is 2‐norbornyl cation (2NB⁺): its existing form (classical or non‐classical) had been debated for decades, until the concrete proof of non‐classical geometry was achieved by X‐ray crystallographic characterization at ultra‐low temperature (40 K) and super acidic environment. However, we lack the understanding about 2NB⁺at ambient conditions. Herein, by taking advantage of the confinement effect and delocalized acidic environment of zeolites, we successfully stabilized 2NB⁺and unequivocally confirmed its “non‐classical” structure inside the ZSM‐5 zeolite byab initiomolecular dynamics simulations and¹³C solid‐state nuclear magnetic resonance experiments. It is the first time to in situ observe the non‐classical 2NB⁺without the super acidic environment at ambient temperature, which provides a new strategy to expand the carbocation chemistry.