Yamabe problem for asymptotically hyperbolic geometries
Abstract: Given a Riemannian manifold, the Yamabe problem seeks to find a metric of constant scalar curvature conformally equivalent to the original metric. For compact manifolds, the problem presents an interesting combination of geometric and analysis challenges. In the asymptotically hyperbolic setting, there are additional challenges associated to the regularity of the conformal boundary. In this talk I explain the nature of these challenges, review existing results, and discuss work that is presently underway.