Convergence of the Weighted Yamabe Flow

Zetian Yan

We introduce the weighted Yamabe flow $\frac{\partial g}{\partial t}=(r_{\varphi }^m-R_{\varphi }^m)g$, $\frac{\partial \varphi }{\partial t}=\frac{m}{2}(R_{\varphi }^m-r_{\varphi }^m)$ on a smooth metric measure space $(M^…