Spectral Geometry Of The Laplacian: Spectral Analysis And Differential Geometry Of The Laplacian

The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is called the spectrum. We describe how the spectrum determines a Riemannian manifold. The continuity of the eigenvalue of the Laplacian, Cheeger and Yau''s estimate of the first eigenvalue, the Lichnerowicz-Obata''s theorem on the first eigenvalue, the Cheng''s estimates of the kth eigenvalues, and Payne-Pólya-Weinb...