Geodesic
Uniformization of strictly pseudoconvex domains.~II
Izvestiya. Mathematics , Tome 69 (2005) no. 6, pp. 1203-1210

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It is shown that if two strictly pseudoconvex Stein domains with real-analytic boundaries have biholomorphic universal coverings, then their boundaries are locally biholomorphically equivalent. 
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     author = {S. Yu. Nemirovski and R. G. Shafikov},
     title = {Uniformization of strictly pseudoconvex {domains.~II}},
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     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2005_69_6_a6/}
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S. Yu. Nemirovski; R. G. Shafikov. Uniformization of strictly pseudoconvex domains.~II. Izvestiya. Mathematics , Tome 69 (2005) no. 6, pp. 1203-1210. http://geodesic.mathdoc.fr/item/IM2_2005_69_6_a6/