In this talk, we will introduce the linearized semigroup for the heat flow and its properties on Finsler manifolds. By means of this linearized semigroup and the ODE technique, we give more general Li-Yau's estimates for the positive solutions to the heat flow on uniform convex and smooth Finsler manifolds with the weighted Ricci curvature bounded from below, which generalize the known Li-Yau's estimates on Finsler (resp. Riemannian) manifolds.

4.23.pdf