Gradient and Eigenvalue Estimates on the Canonical Bundle of Kähler Manifolds

We prove certain gradient and eigenvalue estimates, as well the heat kernel for Hodge Laplacian on (m, 0) forms, i.e., sections of canonical bundle Kähler manifolds, where m is complex dimension manifold. Instead usual dependence curvature tensor, our condition depends only Ricci bound. The proof based a new Bochner type formula which involves scalar curvature.