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Uspekhi Mat. Nauk, 1990, Volume 45, Issue 2(272), Pages 3–47 (Mi umn4714)  

This article is cited in 32 scientific papers (total in 35 papers)

The Riemann–Hilbert problem

A. A. Bolibrukh

Moscow Institute of Physics and Technology

Full text: PDF file (2724 kB)
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English version:
Russian Mathematical Surveys, 1990, 45:2, 1–58

Bibliographic databases:

MSC: 34M50, 34M35
Received: 15.12.1989

Citation: A. A. Bolibrukh, “The Riemann–Hilbert problem”, Uspekhi Mat. Nauk, 45:2(272) (1990), 3–47; Russian Math. Surveys, 45:2 (1990), 1–58

Citation in format AMSBIB
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\yr 1990
\vol 45
\issue 2(272)
\pages 3--47
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\jour Russian Math. Surveys
\yr 1990
\vol 45
\issue 2
\pages 1--58
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Bolibruch, “Vector bundles associated with monodromies and asymptotics of Fuchsian systems”, J Dyn Control Syst, 1:2 (1995), 229  crossref  mathscinet  zmath  elib
    2. A. Bolibrukh, “Holomorphic vector bundles on the Riemann sphere and the 21 st Hilbert problem”, Journal of Mathematical Sciences (New York), 82:6 (1996), 3759  crossref  mathscinet  zmath
    3. A. A. Bolibruch, “On isomonodromic deformations of Fuchsian systems”, J Dyn Control Syst, 3:4 (1997), 589  crossref  mathscinet  zmath  elib
    4. Juliette Vandamme, “Problème de Riemann—Hilbert pour une représentation de monodromie triangulaire supérieure de dimension 5”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 326:9 (1998), 1069  crossref
    5. A. A. Bolibrukh, “On Fuchsian Systems with Given Asymptotics and Monodromy”, Proc. Steklov Inst. Math., 224 (1999), 98–106  mathnet  mathscinet  zmath
    6. A. B. Bogatyrev, “Poincaré–Steklov Integral Equations and the Riemann Monodromy Problem”, Funct. Anal. Appl., 34:2 (2000), 86–97  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. A. B. Bogatyrev, “PS$_3$ integral equations and projective structures on Riemann surfaces”, Sb. Math., 192:4 (2001), 479–514  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. A. A. Bolibrukh, “Obyknovennye differentsialnye uravneniya v problemakh Gilberta”, Matem. prosv., ser. 3, 5, MTsNMO, M., 2001, 20–31  mathnet
    9. Proc. Steklov Inst. Math., 238 (2002), 148–185  mathnet  mathscinet  zmath
    10. A. A. Bolibrukh, “Differential Equations with Meromorphic Coefficients”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S13–S43  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. D. V. Anosov, V. I. Arnol'd, V. M. Buchstaber, V. A. Golubeva, A. A. Gonchar, A. B. Zhizhchenko, Yu. S. Ilyashenko, V. V. Kozlov, S. P. Konovalov, L. D. Kudryavtsev, V. P. Leksin, O. B. Lupanov, A. A. Mal'tsev, E. F. Mishchenko, S. P. Novikov, Yu. S. Osipov, M. M. Postnikov, V. A. Sadovnichii, A. G. Sergeev, L. D. Faddeev, A. V. Chernavskii, “Andrei Andreevich Bolibrukh (obituary)”, Russian Math. Surveys, 58:6 (2003), 1185–1189  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    12. D. V. Anosov, V. P. Leksin, “Andrei Andreevich Bolibrukh in life and science (30 January 1950 – 11 November 2003)”, Russian Math. Surveys, 59:6 (2004), 1009–1028  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    13. Yu. S. Ilyashenko, “Three gems in the theory of linear differential equations (in the work of A. A. Bolibrukh)”, Russian Math. Surveys, 59:6 (2004), 1079–1091  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. C. Sabbah, “Fourier–Laplace transform of irreducible regular differential systems on the Riemann sphere”, Russian Math. Surveys, 59:6 (2004), 1165–1180  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    15. St. Petersburg Math. J., 16:1 (2005), 105–142  mathnet  crossref  mathscinet  zmath
    16. Vladimir Petrov Kostov, “The Deligne–Simpson problem—a survey”, Journal of Algebra, 281:1 (2004), 83  crossref
    17. Vladimir Petrov Kostov, “The Connectedness of Some Varieties and the Deligne—Simpson Problem”, J Dyn Control Syst, 11:1 (2005), 125  crossref  mathscinet  zmath  isi
    18. G. Giorgadze, “On Monodromy of Generalized Analytic Functions”, Journal of Mathematical Sciences (New York), 132:6 (2006), 716  crossref  mathscinet  zmath
    19. Golubeva V.A., “On the Riemann–Hilbert correspondence for generalized Knizhnik–Zamolodchikov equations for different root systems”, Differential Equations and Quantum Groups - ANDREY A. BOLIBRUKH MEMORIAL VOLUME, Irma Lectures in Mathematics and Theoretical Physics, 9, 2007, 189–207  isi
    20. Kostov V.P., “Monodromy groups of regular systems on the Riemann sphere”, Differential Equations and Quantum Groups - ANDREY A. BOLIBRUKH MEMORIAL VOLUME, Irma Lectures in Mathematics and Theoretical Physics, 9, 2007, 209–254  isi
    21. Viktoria Heu, “Stability of rank 2 vector bundles along isomonodromic deformations”, Math Ann, 2008  crossref  mathscinet  isi
    22. R. R. Gontsov, V. A. Poberezhnyi, “Various versions of the Riemann–Hilbert problem for linear differential equations”, Russian Math. Surveys, 63:4 (2008), 603–639  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    23. Novokshenov V.Yu., “The Riemann–Hilbert problem and special functions”, Geometric Methods in Physics, AIP Conference Proceedings, 1079, 2008, 149–161  isi
    24. Eduardo Corel, “Exponents of a meromorphic connection on a compact Riemann surface”, Pacific J Math, 242:2 (2009), 259  crossref  mathscinet  zmath  isi  elib
    25. Alan G. B. Lauder, “Ranks of Elliptic Curves Over Function Fields”, LMS J. Comput. Math, 11 (2010), 172  crossref
    26. D. V. Anosov, V. P. Leksin, “Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations”, Russian Math. Surveys, 66:1 (2011), 1–33  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    27. Arno B. J. Kuijlaars, Man Yue Mo, “The Global Parametrix in the Riemann–Hilbert Steepest Descent Analysis for Orthogonal Polynomials”, Comput. Methods Funct. Theory, 11:1 (2011), 161  crossref
    28. G. Giorgadze, “Some analytical and geometrical aspects of stable partial indices”, J Math Sci, 2013  crossref
    29. Takao Suyama, “A systematic study on matrix models for Chern–Simons-matter theories”, Nuclear Physics B, 2013  crossref
    30. Elie Compoint, Eduardo Corel, “Stable flags, trivializations and regular connections”, Pacific J. Math, 263:2 (2013), 283  crossref
    31. G. Giorgadze, N. Manjavidze, “On some constructive methods for the matrix Riemann–Hilbert boundary-value problem”, J Math Sci, 2013  crossref
    32. Trans. Moscow Math. Soc., 76:2 (2015), 219–236  mathnet  crossref  elib
    33. F. Loray, “Isomonodromic deformation of Lamé connections, Painlevé VI equation and Okamoto symmetry”, Izv. Math., 80:1 (2016), 113–166  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    34. C. Mitschi, “Some applications of parameterized Picard–Vessiot theory”, Izv. Math., 80:1 (2016), 167–188  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    35. Rogosin S., Mishuris G., “Constructive methods for factorization of matrix-functions”, IMA J. Appl. Math., 81:2 (2016), 365–391  crossref  mathscinet  zmath  isi  elib  scopus
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