Horizontal partial derivative-Laplacian on complex Finsler manifolds

A horizontal partial derivative-Laplacian is defined on strongly pseudoconvex complex Finsler manifolds, first for functions and then for horizontal differential forms of type (p,q). The principal part of the partial derivative-Laplacian is computed in local coordinates. As an application, the partial derivative-Laplacian on strongly Kahler Finsler manifold is obtained explicitly in terms of the horizontal covariant derivatives of the Chern-Finsler connection.