Constructive Solvability Conditions for the Riemann-Hilbert Problem
- 39 Downloads
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.
Key wordsRiemann-Hilbert problem Fuchsian system monodromy representation bundle valuation stable pair of a bundle and a logarithmic connection semistable pair of a bundle and a logarithmic connection
Unable to display preview. Download preview PDF.
- 1.A. A. Bolibrukh, “Hilbert’s 21st problem for Fuchsian linear systems,” Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.], 206 (1994).Google Scholar
- 2.V. P. Kostov, “Fuchsian systems on ℂP 1 and the Riemann-Hilbert Problem,” C. R. Acad. Sci. Paris Ser. I, 315 (1992), 143–148.Google Scholar
- 3.A. A. Bolibrukh, Fuchsian Differential Equations and Holomorphic Bundles [in Russian], MTsNMO, Moscow, 2000.Google Scholar
- 4.A. A. Bolibrukh, “The Riemann-Hilbert problem on a compact Riemann surface,” Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.], 238 (2002), 55–69.Google Scholar
- 6.S. Malek, “Systemes fuchsiens a monodromie reductible,” C. R. Acad. Sci. Paris Ser. I, 332 (2001), no. 8, 691–694.Google Scholar