Prescribing Gaussian and Geodesic Curvature on Disks
Prescribing Gaussian and Geodesic Curvature on Disks
Abstract In this paper, we consider the problem of prescribing the Gaussian and geodesic curvature on a disk and its boundary, respectively, via a conformal change of the metric. This leads us to a Liouville-type equation with a non-linear Neumann boundary condition. We address the question of existence by setting …