Escobar-Yamabe compactifications for Poincare-Einstein manifolds and rigidity theorems

Xuezhang Chen, Mijia Lai, Fang Wang

Let $(X^n,g_{+})$ $(n\ge 3)$ be a Poincaré-Einstein manifold which is $C^{3,\alpha }$ conformally compact with conformal infinity $(\partial X,[\hat{g}])$. On the conformal compactifi…