Bochner-Weitzenb\"ock formula and Li-Yau estimates on Finsler manifolds

We prove the Bochner-Weitzenb"ock formula for the (nonlinear) Laplacian on general Finsler manifolds and derive Li-Yau type gradient estimates as well as parabolic Harnack inequalities. Moreover, we deduce Bakry-'Emery gradient estimates. All these estimates depend on lower bounds for the weighted flag Ricci tensor.