Constructive Solvability Conditions for the Riemann-Hilbert Problem
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
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