PRESCRIBING THE BOUNDARY GEODESIC CURVATURE ON A COMPACT SCALAR-FLAT RIEMANN SURFACE VIA A FLOW METHOD

摘要

We study the problem of prescribing the boundary geodesic curvature on a compact scalar-flat Riemann surface. We use the negative gradient flow method. We prove the global existence and the convergence of the flow as time goes to infinity under sufficient conditions on the prescribed function.