New Differential Harnack Inequalities for Nonlinear Heat Equations
Jiayong Wu
Chinese Annals of Mathematics, Series B ›› 2020, Vol. 41 ›› Issue (2) : 267 -284.
New Differential Harnack Inequalities for Nonlinear Heat Equations
This paper deals with constrained trace, matrix and constrained matrix Harnack inequalities for the nonlinear heat equation ω t = Δω + aω ln ω on closed manifolds. A new interpolated Harnack inequality for ω t = Δω − ω ln ω+εRω on closed surfaces under ε-Ricci flow is also derived. Finally, the author proves a new differential Harnack inequality for ω t = Δω − ω ln ω under Ricci flow without any curvature condition. Among these Harnack inequalities, the correction terms are all time-exponential functions, which are superior to time-polynomial functions.
Harnack inequality / Nonlinear heat equation / Ricci flow
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