This article is cited in 4 papers

Constructive Solvability Conditions for the Riemann–Hilbert Problem

I. V. Vyugin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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.

UDC: 512.772.3+517.927.7

Received: 20.02.2004
Revised: 07.04.2004

DOI: 10.4213/mzm2535

 English version: Mathematical Notes, 2005, 77:5, 595–605

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