A conformally invariant sphere theorem in four dimensions

2003/09/17 by S. Y. A Chang, Chang, S. Y. A, Matthew J. Gursky +3 · 1 citation
Mathematics · #53C20 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C20

paper · pdf · doi:10.48550/arxiv.math/0309287

39 pages, 0 figures

arxiv created 2003/09/17 · arxiv updated 2009/12/01

Abstract

In this paper we provide a sharp characterization of the smooth four-dimensional sphere. The assumptions of the theorem are conformally invariant, and can be reduced to an L² inequality of the Weyl tensor and positivity of the Yamabe invariant.

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