Hamilton-Souplet-Zhang’s Gradient Estimates for Two Types of Nonlinear Parabolic Equations under the Ricci Flow

Abstract

We consider gradient estimates for two types of nonlinear parabolic equations under the Ricci flow: one is the equationut=Δu+aulog⁡u+buwitha,bbeing two real constants; the other isut=Δu+λuαwithλ,αbeing two real constants. By a suitable scaling for the above two equations, we obtain Hamilton-Souplet-Zhang-type gradient estimates.