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HARNACK ESTIMATES FOR NONLINEAR BACKWARD HEAT EQUATIONS WITH POTENTIALS ALONG THE RICCI-BOURGUIGNON FLOW

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In this paper, we derive various differential Harnack estimates for positive solutions to the nonlinear backward heat type equations on closed manifolds coupled with the Ricci-Bourguignon flow, which was done… Click to show full abstract

In this paper, we derive various differential Harnack estimates for positive solutions to the nonlinear backward heat type equations on closed manifolds coupled with the Ricci-Bourguignon flow, which was done for the Ricci flow by J.-Y. Wu [30]. The proof follows exactly the one given by X.-D. Cao [4] for the linear backward heat type equations coupled with the Ricci flow.

Keywords: ricci; heat; harnack estimates; backward heat; nonlinear backward; flow

Journal Title: Journal of The Korean Mathematical Society
Year Published: 2020

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