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 \cite{CGY}. Moreover, it provides a four-dimensional analogue of the well-known classification theorem of Schoen-Yau \cite{SY2} on 3-manifolds with positive Yamabe invariants.

18 pages. we supplement the reducible case b) in rigidity theorem 1.6 and add more references in the new version