Rigidity of proper holomorphic mappings between equidimensional bounded symmetric domains (Q2781250)

The author shows that if \(\Omega_1,\Omega_2\) are two bounded symmetric domains of the same dimension and \(\Omega_1\) is irreducible and of rank\({}>1\), then any proper holomorphic mapping from \(\Omega_1\) into \(\Omega_2\) is a biholomorphism. This generalizes the result of \textit{G. M. Henkin} and \textit{R. G. Novikov} for \(\Omega_1=\Omega_2\) [see p. 625-627 of the problem book in Lect. Notes Math. 1043 (1984; Zbl 0545.30038)], and also complements the results of \textit{E. Bedford} and \textit{S. Bell} [Math. Ann. 261, 47-49 (1982; Zbl 0499.32016)] and \textit{K. Diederich} and \textit{J. E. Fornæss} [Math. Ann. 259, 279-286 (1982; Zbl 0486.32013)] for smoothly bounded pseudoconvex domains.