Geodesic
Constructive Solvability Conditions for the Riemann–Hilbert Problem
Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 643-655 
I. V. Vyugin. Constructive Solvability Conditions for the Riemann–Hilbert Problem. Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 643-655. http://geodesic.mathdoc.fr/item/MZM_2005_77_5_a0/
@article{MZM_2005_77_5_a0,
     author = {I. V. Vyugin},
     title = {Constructive {Solvability} {Conditions} for the {Riemann{\textendash}Hilbert} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--655},
     year = {2005},
     volume = {77},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_5_a0/}
}
TY  - JOUR
AU  - I. V. Vyugin
TI  - Constructive Solvability Conditions for the Riemann–Hilbert Problem
JO  - Matematičeskie zametki
PY  - 2005
SP  - 643
EP  - 655
VL  - 77
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_2005_77_5_a0/
LA  - ru
ID  - MZM_2005_77_5_a0
ER  - 
%0 Journal Article
%A I. V. Vyugin
%T Constructive Solvability Conditions for the Riemann–Hilbert Problem
%J Matematičeskie zametki
%D 2005
%P 643-655
%V 77
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_2005_77_5_a0/
%G ru
%F MZM_2005_77_5_a0

Voir la notice de l'article provenant de la source Math-Net.Ru

Sufficient and necessary conditions for the solvability of the Riemann–Hilbert problem are studied. These conditions consist in the possibility of constructing stable and semistable pairs (of bundles and connections) for a given monodromy. The obtained results make it possible to develop algorithms for testing the solvability conditions for the Riemann–Hilbert problem.

[1] Bolibrukh A. A., 21-ya problema Gilberta dlya lineinykh fuksovykh sistem, Tr. MIAN, 206, Nauka, M., 1994 | MR | Zbl

[2] Kostov V. P., “Fuchsian systems on $\mathbb{C}P^1$ and the Riemann–Hilbert Problem”, C. R. Acad. Sci. Paris Sér. I, 315 (1992), 143–148 | MR | Zbl

[3] Bolibrukh A. A., Fuksovy differentsialnye uravneniya i golomorfnye rassloeniya, MTsNMO, M., 2000

[4] Bolibrukh A. A., “Problema Rimana–Gilberta na kompaktnoi rimanovoi poverkhnosti”, Tr. MIAN, 238, Nauka, M., 2002, 55–69

[5] Gladyshev A. I., “On the Riemann–Hilbert problem in dimention 4”, J. Dynamical Control Systems, 6:2 (2000), 219–264 | DOI | MR | Zbl

[6] Malek S., “Systèmes fuchsiens à monodromie réductible”, C. R. Acad. Sci. Paris Sér. I, 332:8 (2001), 691–694 | Zbl