Li-Yau's Estimates on Finsler Manifolds

In this paper, we give new Li-Yau's type gradient estimates for the positive solutions to the nonlinear heat flow on compact Finsler manifolds with boundary (possibly the boundary is empty) or complete noncompact Finsler manifolds under the assumption that the weighted Ricci curvature is bounded from below. As applications, we obtain the Harnack and mean value inequalities on these manifolds.