A gradient estimate is proved for the parabolic PDE on warping functions that arises as the evolution condition for warped metrics under the Ricci-Bourguignon flow.
Convergence of Ricci flow on a class of warped product metrics.The Journal of Geometric Analysis, 30(4):4036–4070
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Gradient estimates for a parabolic partial differential equation under the Ricci-Bourguignon flow
A gradient estimate is proved for the parabolic PDE on warping functions that arises as the evolution condition for warped metrics under the Ricci-Bourguignon flow.