A conformally invariant classification theorem in four dimensions

Abstract

In this paper, we prove a classification theorem of 4-manifolds according to some conformal invariants, which generalizes the conformally invariant sphere theorem of Chang-Gursky-Yang [2]. Moreover, it provides a four-dimensional analog of the well-known classification theorem of Schoen-Yau [18, 19] on 3-manifolds with positive Yamabe invariants.