Bochner-Weitzenboeck formula and Li-Yau estimates on Finsler manifolds
  We prove the Bochner-Weitzenboeck 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. 
Shin-ichi Ohta and Karl-Theodor Sturm
math.AP