Evolution of the Yamabe constant under Bernhard List's flow

Let $g(t)$ be a solution of Bernhard List's flow on a closed manifold. We obtain a pointwise control on the volume of $g(t)$. Then under an essential assumption, we achieve a formula for the evolution of the Yamabe constant $\mathscr Y(g(t))$ when $g(t)$ is evolving by Bernhard List's flow.