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

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