On the Riemann-Hilbert Problems

Details On the Riemann-Hilbert Problems On the Riemann-Hilbert Problems

1998-04-07

arxiv.org/abs/math/9804035v1

Mathematics

Complex Variables

40 pages

Scientific paper

We discuss some topological aspects of the Riemann-Hilbert transmission problem and Riemann-Hilbert monodromy problem on Riemann surfaces. In particular, we describe the construction of a holomorphic vector bundle starting from the given representation of the fundamental group and investigate the local behaviour of connexions on this bundle. We give formulae for the partial indices of the Riemann-Hilbert transmission problem in the three-dimensional case in terms of the correspoding vector bundle on the Riemann sphere.

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