Harnack estimates for nonlinear backward heat equations with potentials along the Ricci-Bourguignon flow
J. Korean Math. Soc.
Published online September 18, 2019
Jianhong Wang
East China Normal University
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 : Harnack estimate, nonlinear backward heat type equation, Ricci-Bourguignon flow, blow up
MSC numbers : 53C44
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