1. some example and observations $latex {(M^2,g)}&fg=000000$,$latex {g(t)=e^{2u(t)}g_0}&fg=000000$, $latex \displaystyle \frac{\partial u}{\partial t}=e^{-2u}\tilde\Delta u+\frac{r}{2}-e^{-2u}K_0 &fg=000000$ $latex {(M^n,g_{ij}(t))}&fg=000000$ $latex \displaystyle \frac{\partial g_{ij}(t)}{\partial t}=-2Ric(g_{ij})&fg=000000$ The given “smooth” initial : $latex {\exists }&fg=000000$ T small ,$latex {T>0}&fg=000000$,the solution exists on $latex {[0,T]}&…
