In this talk, I will discuss about the distribution of eigenvalues of the weighted Laplacian on closed weighted Riemannian manifolds of nonnegative Bakry-Emery Ricci curvature. As an application of the curvature dimension condition, I will derive some universal inequalities among eigenvalues of the weighted Laplacian on such manifolds. These inequalities are quantitative versions of the previous theorem by the author with Shioya. I will also discuss some geometric quantity, called multi-way isoperimetric constants, on such manifolds and obtain similar universal inequalities among them. Multi-way isoperimetric constants are generalizations of the Cheeger constant. I will explain the relation between the $k$-th eigenvalue and the $k$-way isoperimetric constant.
