On some polynomially convex maximal real submanifolds in and a related Riemann–Hilbert problem

It is proved that certain maximal real graphs of maps from C n to C n are polynomially convex. Manifolds fibred over ∂Δ, with fibres being such graphs, are introduced and a related Riemann–Hilbert problem is considered. Existence of a solution is proved, and its local structure is studied.