Partial differential equations play an important role in conformal geometry. Our recent study focuses on using potential theory to study such PDEs. I will talk about my joint works with professor Jie Qing, inculding how to describe the end structure of locally conformally flat manifolds, how to generalize Huber’s theory to higher dimensions and how to generalize a result of Schoen and Yau, about the dimension of the boundary of a domain on $S^n$, with a complete, nonnegative scalar curvature conformal metric on it.