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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.
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참고문헌 (36)
참고문헌 신청
B. Andrews / 1994 / Harnack inequalities for evolving hypersurfaces / Math. Z 217(2):179~197
J.-P. Bourguignon / 1981 / Ricci curvature and Einstein metrics, in Global dierential geometry and global analysis / Lecture Notes in Math 838
H. -D. Cao / 1992 / On Harnack's inequalities for the Kahler-Ricci ow / Invent. Math 109(2):247~263
X. Cao / 2008 / Dierential Harnack estimates for backward heat equations with potentials under the Ricci ow / J. Funct. Anal 255(4):1024~1038
X. Cao / 2015 / Harnack estimates for conjugate heat kernel on evolving manifolds / Math. Z 281(1-2):201~214
J.-P. Bourguignon / 1981 / Ricci curvature and Einstein metrics, in Global dierential geometry and global analysis / Lecture Notes in Math 838
H. -D. Cao / 1992 / On Harnack's inequalities for the Kahler-Ricci ow / Invent. Math 109(2):247~263
X. Cao / 2008 / Dierential Harnack estimates for backward heat equations with potentials under the Ricci ow / J. Funct. Anal 255(4):1024~1038
X. Cao / 2015 / Harnack estimates for conjugate heat kernel on evolving manifolds / Math. Z 281(1-2):201~214
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