| Résume | Given a Riemannian manifold $(M^n,g)$ with a metric of rough regularity, is it possible to deform it into a smooth Riemannian manifold via a conformal diffeomorphism? The aim of the talk is to give a precise answer to this question, to relate it to the Yamabe problem for rough metrics, and to show some applications in conformal geometry and general relativity. In particular, we establish global regularity results for constant scalar curvature metrics, conformally flat metrics, and static spacetimes. This is based on joint work with Rodrigo Avalos and Albachiara Cogo. |
