The Dirichlet Problem for The Prescribed Ricci Curvature Equation
We will discuss the following question: is it possible to find a Riemannian metric with given Ricci curvature on a manifold M? To answer this question, one must analyze a weakly elliptic second-order partial differential equation for tensors. In the first part of the talk, we will review the relevant background and the history of the subject. After that, our focus will be on new results concerning the case where M is a bounded domain in a cohomogeneity one manifold.