| This paper investigate the eigenvalues for the drifting Laplacian on the bounded domain on noncompact Riemannian manifolds.By using upper half-plane model,we establish an universal inequality for incomplete drifting Laplacian on the hyperbolic space,which can be viewed as a rigidity result associated with variable.Applying comparison geometry,we obtain some eigenvalue inequalities for sectional curvature.In particular,when the radial symmetric potential function is exactly distance function,we obtain an eigenvalue inequality,which is universal.Finally,by controlling the bound for the distance function,we have establish eigenvalue inequalities without the radial symmetric assumption and the condition of the Bakry-′Emery Ricci curvature. |
