Geodesic
Uniformization of strictly pseudoconvex domains.~I
Izvestiya. Mathematics , Tome 69 (2005) no. 6, pp. 1189-1202.

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It is shown that two strictly pseudoconvex Stein domains with real-analytic boundaries have biholomorphic universal coverings provided that their boundaries are locally biholomorphically equivalent. This statement can be regarded as a higher-dimensional analogue of the uniformization theorem. 
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S. Yu. Nemirovski; R. G. Shafikov. Uniformization of strictly pseudoconvex domains.~I. Izvestiya. Mathematics , Tome 69 (2005) no. 6, pp. 1189-1202. http://geodesic.mathdoc.fr/item/IM2_2005_69_6_a5/

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