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## Стабильные расслоения и проблема Римана–Гильберта на римановой поверхности

The paper is devoted to the study of holomorphic vector bundles with logarithmic connections on a compact Riemann surface and the application of the results obtained to the study of the question of positive solvability of the Riemann–Hilbert problem on a Riemann surface. We give an example of a representation of the fundamental group of a Riemann surface with four punctured points, which cannot be realized as a monodromy representation of a logarithmic connection with four singular points in any semistable bundle. For an arbitrary pair - a bundle and a logarithmic connection in it—we prove an estimate for the slopes of the associated Harder–Narasimhan filtration factors. In addition, we present some results on the realizability of the representation as a direct summand in the monodromy representation of a logarithmic connection in a semistable bundle of degree zero.