Communications in Analysis and Geometry

Volume 22 (2014)

Number 5

A conformally invariant classification theorem in four dimensions

Pages: 811 – 831

DOI: https://dx.doi.org/10.4310/CAG.2014.v22.n5.a2

Authors

Bing-Long Chen (Department of Mathematics, Sun Yat-Sen University, Guangzhou, China)

Xi-Ping Zhu (Department of Mathematics, Sun Yat-Sen University, Guangzhou, China)

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. Moreover, it provides a four-dimensional analog of the well-known classification theorem of Schoen-Yau on 3-manifolds with positive Yamabe invariants.

Published 29 October 2014