Yamabe problem states that:
Given a smooth, compact manifold $M$ of dimension $n \geq 3$ with a Riemannian metric $g$, does there exist a metric $h$ conformal to $g$ for which the scalar curvature of $h$ is constant?
The answer is now known to be yes and I want to know
Question: Does the proof of Yamabe problem give a method for finding metric of constant scalar curvature? If the answer is positive, then what is its method?
Thanks.