6 dec 2018 -- 16:30
Aula Tricerri, DiMaI, Firenze
The Yamabe problem on compact smooth manifolds has been one of the starting point of geometric analysis. It consists in showing, with both geometric and analytic tools, that there always exists a Riemmanian metric with constant scalar curvature in the conformal class of a given metric (N. Trudinger, T. Aubin, R. Schoen). When considering a manifold with singularities, it is not always possible to find such a metric. In this talk, we will focus on manifolds with conical singularities, isolated or not, and we will underline the issues arising when trying to solve the Yamabe problem. We will present some results of existence and non-existence of conformal metrics with constant scalar curvature in the singular setting. Part of the talk is based on a joint work with K. Akutagawa.