Variation formula for eigenvalues of Laplace-Beltrami under the Kähler-Ricci flow

In this article we will consider the eigenvalue problem for the Laplace-Beltrami operator acting on the space of functions on closed Kähler manifolds. We find the first variation formula for the eigenvalues of Laplace-Beltrami on a closed Kähler-manifold evolving under the Kähler-Ricci flow and show that the eigenvalues of Laplace-Beltrami on $(M^1, g(t))$ with positive Ricci curvature is .increasing and find some applications