This talk is based on my Master’s Thesis work in Bologna, under the supervision of Prof. Vittorio Martino. We shall discuss the proof of what we have referred to as the "Resolution Criterion" for the Yamabe problem — namely, the proof by Trudinger and Aubin that the Yamabe problem admits a solution on any manifold whose Yamabe invariant is strictly less than that of the standard sphere. Furthermore, we shall discuss additional aspects of the problem in the case of the standard sphere itself, related to the uniqueness of the solution in this specific setting.
