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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 6, Pages 115–130 (Mi izv668)  

This article is cited in 11 scientific papers (total in 11 papers)

Uniformization of strictly pseudoconvex domains. I

S. Yu. Nemirovskia, R. G. Shafikovb

a Steklov Mathematical Institute, Russian Academy of Sciences
b University of Western Ontario, Department of Mathematics

Abstract: 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.

DOI: https://doi.org/10.4213/im668

Full text: PDF file (1899 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2005, 69:6, 1189–1202

Bibliographic databases:

Document Type: Article
UDC: 517.55
MSC: 32D15, 32D10, 32E10
Received: 10.03.2005

Citation: S. Yu. Nemirovski, R. G. Shafikov, “Uniformization of strictly pseudoconvex domains. I”, Izv. RAN. Ser. Mat., 69:6 (2005), 115–130; Izv. Math., 69:6 (2005), 1189–1202

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    This publication is cited in the following articles:
    1. S. Yu. Nemirovski, R. G. Shafikov, “Uniformization of strictly pseudoconvex domains. II”, Izv. Math., 69:6 (2005), 1203–1210  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. S. Yu. Nemirovski, R. G. Shafikov, “Conjectures of Cheng and Ramadanov”, Russian Math. Surveys, 61:4 (2006), 780–782  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Isaev A.V., Kossovskiy I.C., “Continuation of CR-automorphisms of Levi degenerate hyperquadrics to the projective space”, Illinois J. Math., 54:2 (2010), 747–752  mathscinet  zmath  isi  elib
    4. Isaev A., Spherical tube hypersurfaces, Lecture Notes in Math., 2020, Springer, Heidelberg, 2011, xii+220 pp.  crossref  mathscinet  zmath  isi  scopus
    5. A. V. ISAEV, “ON THE CLASSIFICATION OF HOMOGENEOUS HYPERSURFACES IN COMPLEX SPACE”, Int. J. Math, 2013, 1350064  crossref  mathscinet  zmath  isi  elib  scopus
    6. A.V. Isaev, “On a family of real hypersurfaces in a complex quadric”, Differential Geometry and its Applications, 2013  crossref  mathscinet  isi  scopus
    7. Jae-Cheon Joo, Aeryeong Seo, “HIGHER ORDER ASYMPTOTIC BEHAVIOR OF CERTAIN KÄHLER METRICS AND UNIFORMIZATION FOR STRONGLY PSEUDOCONVEX DOMAINS”, Journal of the Korean Mathematical Society, 52:1 (2015), 113  crossref  mathscinet  zmath  scopus
    8. Zhang L., “On Curvature Estimates of Bounded Domains”, Complex Analysis and Geometry, Springer Proceedings in Mathematics & Statistics, Springer Proceedings in Mathematics & Statistics, 144, eds. Bracci F., Byun J., Gaussier H., Hirachi K., Kim K., Shcherbina N., Springer, 2015, 353–367  crossref  mathscinet  zmath  isi  scopus
    9. S. Pinchuk, R. Shafikov, A. Sukhov, “Some Aspects of Holomorphic Mappings: A Survey”, Proc. Steklov Inst. Math., 298 (2017), 212–247  mathnet  crossref  crossref  isi  elib
    10. Zhang L., “Intrinsic Derivative, Curvature Estimates and Squeezing Function”, Sci. China-Math., 60:6, SI (2017), 1149–1162  crossref  mathscinet  zmath  isi  scopus
    11. Nemirovski S. Shafikov R.G., “Uniformization and Steinness”, Can. Math. Bul.-Bul. Can. Math., 61:3 (2018), 637–639  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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