G. Giorgadze

Riemann-Hilbert Problems and Yang-Mills Theory

abstract:
Two-dimensional Yang-Mills equations on Riemann surfaces and Bogomol'ny equation are studied using methods of the theory of Riemann-Hilbert problem. In particular, representations of solutions in terms of connections are given and solvability conditions of arising Riemann-Hilbert problems are established.

Mathematics Subject Classification: 30E25, 32L05

Key words and phrases: Riemann-Hilbert problem, Riemann surface, holomorphic bundle, meromorphic connection, monodromy, Yang-Mills equations