Using non-linear connection of Finsler manifold M, the existence of localcoordinates which is normalized at a point x is proved, and the Laplace operator △ on1-form of M is defined by non-linear connection and its curvature tensor. After proving themaximum principle theorem of Hopf-Bochner on M, the Bochner type vanishing theoremof Killing vectors and harmonic 1-form are obtained.
A new Koppelman-Leray-Norguet formula of (p, q) differential forms for astrictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein man-ifold is obtained, and an integral representation for the solution of a-equation on thisdomain which does not involve integrals on boundary is given, so one can avoid complexestimates of boundary integrals.
