The prescribed boundary mean curvature problem on the standard image-dimensional ball Review Article

In this paper, we consider a boundary value problem associated with the conformal deformation of metrics on the unit ball Bn,n≥3Bn,n≥3. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we prove the existence of a metric, conformally equivalent to the Euclidean metric, with zero scalar curvature and prescribed mean curvature on the boundary.