Almir Rogério Silva Santos

The resolution of The Yamabe Problem showed that every n-dimensional compact Riemannian manifold, $n>2$, has a conformal metric of constant scalar curvature. It is then natural to ask whether every noncompact Riemannian manifold of dimension $n>2$ is conformally equivalent to a complete manifold with constant scalar curvature. For noncompact manifolds with a simple structure at infinity, this question may be studied by solving the so-called Singular Yamabe Problem. In this talk I will present the main results known about the singular Yamabe problem and I will show how to use perturbation techiniques and gluing methods to produce solutions to this problem.