Some explicit solutions to the Riemann-Hilbert problem

Abstract

Explicit solutions to the Riemann-Hilbert problem will be found realising some irreducible non-rigid local systems. The relation to isomonodromy and the sixth Painleve equation will be described. Keywords: Riemann-Hilbert problem, Painleve equations, algebraic solutions, Heun equations, tetrahedral/octahedral group, triangle groups, Belyi maps.

24 pages, 4 tables (more details, references updated)

References in corpus (1)

• Dessins d'Enfants, Their Deformations and Algebraic the Sixth Painlevé and Gauss Hypergeometric Functions

Cited by in corpus (3)

• Six results on Painleve VI
• Remarks Towards the Classification of $R{S}_4^2(3)$-Transformations and Algebraic Solutions of the Sixth Painlevé Equation
• Schlesinger transformations for algebraic Painleve VI solutions