Universal inequalities on complete noncompact smooth metric measure spaces

Abstract

In this paper, we obtain universal inequalities for the eigenvalues of the Dirichlet problem and clamped plate problem of drifting Laplacian on ( $$n+1$$ )-dimensional ( $$n\ge 4$$ ) complete noncompact simply connected smooth metric measure spaces which meet some conditions of the sectional curvature and radial weighted Ricci curvature.