Title: A complete variational theory for Yamabe type problems.

Abstract: In this talk, we will present a complete variational theory for Yamabe type problems. We will show how the combination of the Aubin-Schoen’s minimizing technique and the Bahri-Coron ’s barycenter technique leads to a natural solution for such problems without any Positive Mass type assumption or variant of it. To emphasize the main ideas of the theory, we will focus on the Fractional Yamabe problem on conformal infinity of Poincare-Einstein manifolds with parameter ã ∈ (1, 2) discussing a joint work with Y. Sire and L. Sun.