On the classification of static three-manifolds with positive scalar curvature

A Riemannian manifold is called static when it admits a non-trivial solution to a certain equation that appears both in Geometry (e.g, in the problem of prescribing the scalar curvature) and in Physics (e.g., in the study of static space-times). The staticity condition is very restrictive, specially in dimension three. We will discuss some classification results in the positive scalar curvature case.