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.
Gradient Einstein-type warped products: Rigidity, existence and nonexistence results via a nonlinear PDE.Nonlinear Analysis, 255:113759
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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.