On the curvature estimates for the conformal Ricci flow. (English) Zbl 1461.53069
Summary: 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.
MSC:
| 53E20 | Ricci flows |
| 58J99 | Partial differential equations on manifolds; differential operators |
| 53C18 | Conformal structures on manifolds |
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