Yamabe constant evolution and monotonicity along the conformal Ricci flow

We investigate the Yamabe constant's behaviour in a conformal Ricci flow. For conformal Ricci flow metric $g(t)$, $t\in [0,T)$, the time evolution formula for the Yamabe constant $Y(g(t))$ is derived. It is demonstrated that if the beginning metric $g(0)=g_0$ is Yamabe metric, then the Yamabe constant is monotonically growing along the conformal Ricci flow under some simple assumptions unless $g_0$ is Einstein. As a result, this study adds to the body of knowledge about the Yamabe problem.