Gradient estimates for a nonlinear parabolic equation under Ricci flow

2008/06/25 by Hsu, Shu-Yu
#58J05 #58J35 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0806.4004

Abstract

Let (M,g(t)), 0≤ t≤ T, be a n-dimensional complete noncompact manifold, n≥ 2, with bounded curvatures and metric g(t) evolving by the Ricci flow \frac∂ g_ij∂ t=-2R_ij. We will extend the result of L. Ma and Y. Yang and prove a local gradient estimate for positive solutions of the nonlinear parabolic equation (\1 u)/(\1 t)=Δu-aulog u-qu where a∈\R is a constant and q is a smooth function on M× [0,T].

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