Riemann-Hilbert problems with constraints

TL;DR

This paper investigates Riemann-Hilbert problems with constraints, providing criteria for solution existence and space dimension, and applying these results to construct analytic discs attached to singular manifolds.

Contribution

It introduces new characterizations of solutions to constrained Riemann-Hilbert problems and demonstrates their application in complex geometry.

Findings

Characterization of solution existence based on indices

Determination of solution space dimension

Application to constructing analytic discs on singular manifolds

Abstract

This paper is devoted to Riemann-Hilbert problems with constraints. We obtain results characterizing the existence of solutions as well as the dimension of the solution space in terms of certain indices. As an application, we show how such results may be used to construct analytic discs attached to singular manifolds.