Eigenvalue estimates for certain noncompact manifolds (Q1074935)

Estimates for the number N(\(\lambda)\) of eigenvalues of the Laplacian \(\Delta\) on a noncompact complete Riemannian manifold X are derived. One assumes that X has a finite number of ends and that either (i) each end is cylindrical or (ii) each end is isometric to an end in a locally symmetric space of Q-rank 1. Then the main result asserts that N(\(\lambda)\) has at most polynomial growth in \(\lambda\).