2018-05-09 14:30-16:30 Room 1556, Science building No.1 I will talk about two types of Escobar-Yamabe compactification for Poincare-Einstein manifolds and derive some inequalities between the Yamabe constants for the conformal class of compactified metric and the Yamabe constant for the conformal infinity. Based on thoses inequalities, I will also give some rigidity theorems. This work was motivated by recent work of Gursky-Han, and collaborated with M. Lai and X. Chen.