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…

Let $\gamma \in (0,1)$, $n > 2\gamma$, and let $(X^{n+1},g^+)$ be Poincaré–Einstein. Suppose that $\Lambda^{\gamma}(M,[\hat{h}])>0$ and that either $(M^n,[\hat{h}])$ is locally con…