Some aspects of Ricci flow on the 4-sphere

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In this paper, on 4-spheres equipped with Riemannian metrics we study some integral conformal invariants, the sign and size of which under Ricci flow characterize the standard 4-sphere. We obtain a conformal gap theorem, and for Yamabe metrics of positive scalar curvature with the L2norm of the Weyl tensor of the metric suitably small, we establish the monotonic decay of the Lpnorm for certain p > 2 of the reduced curvature tensor along the normalized Ricci flow, with the metric converging exponentially to the standard 4-sphere.

Original languageEnglish (US)
Pages (from-to)381-402
Number of pages22
JournalNew Zealand Journal of Mathematics
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics
  • Geometry and Topology
  • Algebra and Number Theory


  • Conformal invariants
  • Gap theorem
  • Ricci flow


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