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.
Sharp gradient estimate and Yau’s Liouville theorem for the heat equation on noncompact manifolds.Bulletin of the London Mathematical Society, 38(6):1045–1053
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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.