Conformal Green functions and Yamabe metrics of Sobolev regularity

Rodrigo Avalos, Albachiara Cogo, Andoni Royo Abrego

We provide a full resolution of the Yamabe problem on closed 3-manifolds for Riemannian metrics of Sobolev class $W^{2,q}$ with $q>3$. This requires developing an elliptic theory…