On the curvature estimates for the conformal Ricci flow

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Original languageEnglish
Article number124965
Journal / PublicationJournal of Mathematical Analysis and Applications
Issue number2
Online published15 Jan 2021
Publication statusPublished - 15 Jun 2021


In this paper, we study the curvature estimates of the conformal Ricci flow on Riemannian manifolds. We show that the norm of the Weyl tensors of any smooth solution to the conformal Ricci flow can be explicitly estimated in terms of its initial values on a given ball, a local uniform bound on the Ricci tensors, and the potential function. On the compact manifold, the curvature operator remains bounded so long as the Ricci curvature is bounded.

Research Area(s)

  • Conformal Ricci flow, Curvature estimates