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 equation ut=Δu+aulog⁡u+bu with a,b being two real constants; the other is ut=Δu+λuα with λ,α being two real constants. By a suitable scaling for the above two equations, we obtain Hamilton-Souplet-Zhang-type gradient estimates.