Abstract
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.
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I dedicate this work to the blessed memory of my teacher Andrei Andreevich Bolibrukh
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Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 643–655.
Original Russian Text Copyright ©2005 by I. V. V’yugin.
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V’yugin, I.V. Constructive Solvability Conditions for the Riemann-Hilbert Problem. Math Notes 77, 595–605 (2005). https://doi.org/10.1007/s11006-005-0061-8
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DOI: https://doi.org/10.1007/s11006-005-0061-8