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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2020; 57(2): 313-329

Online first article September 18, 2019      Printed March 1, 2020

https://doi.org/10.4134/JKMS.j190049

Copyright © The Korean Mathematical Society.

Harnack estimates for nonlinear backward heat equations with potentials along the Ricci-Bourguignon flow

Jian-Hong Wang

East China Normal University

Abstract

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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 for the Ricci flow by J.-Y. Wu \cite{[WJY12]}. The proof follows exactly the one given by X.-D. Cao \cite{[CXD08]} 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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