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In this paper, we study the Ricci flow on closed manifolds equipped withwarped product metric $(N\times F,g_{N}+f^2 g_{F})$ with $(F,g_{F})$ Ricciflat. Using the framework of monotone formulas, we derive several estimates forthe adapted heat conjugate fundamental solution which include an analog of G.Perelman's differential Harnack inequality.

Harnack Estimates for Ricci Flow on a Warped Product