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 (3)

• Transformations ${RS}_4^2(3)$ of the Ranks $\le 4$ and Algebraic Solutions of the Sixth Painlevé Equation
• Bäcklund Transformations of the Sixth Painlevé Equation in Terms of Riemann-Hilbert Correspondence
• Dessins d'Enfants, Their Deformations and Algebraic the Sixth Painlevé and Gauss Hypergeometric Functions

Cited by in corpus (14)

• Flat Structure on the Space of Isomonodromic Deformations
• Computation of highly ramified coverings
• Six results on Painleve VI
• Apparent singularities of Fuchsian equations, and the Painlevé VI equation and Garnier systems
• Classification of algebraic solutions of irregular Garnier systems
• 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
• Solutions algébriques. Solutions algébriques partielles des équations isomonodromiques sur les courbes de genre $2$
• Computation of RS-pullback transformations for algebraic Painleve VI solutions
• Symmetric cubic surfaces and G_2 character varieties
• Construction et classification de certaines solutions algébriques des systèmes de Garnier
• Differential relations for almost Belyi maps
• Higher genus icosahedral Painleve curves
• The fifty-two icosahedral solutions to Painleve VI