2 problems

Let $(X^N,g_+)$, with $N=n+1\ge 3$, be a smooth Poincaré–Einstein manifold with conformal infinity $(M^n,[h])$. Assume that $Y(M,[h])>0$, and let $(\overline X,[\bar g])$ denote it…

Hebey–Vaugon conjecture. If $(M^n,g)$ is not conformal to the standard metric on $S^n$, or if the action of $G$ has no fixed point, then