"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 Li…
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 Lic…
Nonlinear dynamical systems of mathematical physics: spectral and symplectic integrability analysis
by Samoylenko, Valeriy Hr, Blackmore, Denis, Prykarpatsky, Anatoliy K., Mathematiker, Ukraine, Prykarpatsky, Anatoliy K., Mathematician, Ukraine, Prykarpatsky, Anatoliy K., Mathématicien, Ukraine
This work presents some classical as well as some very recent results and techniques concerning the spectral geometry corresponding to the Laplace-Beltrami operator and the Hodge-de Rham operators. It treats many topics that are not usually dealt with in this field.
It is known that to any Riemannian manifold (M, g), with or without boundary, one can associate certain fundamental objects. Among them are the Laplace-Beltrami operaƯ tor and the Hodge-de Rham operators, which are natural [that is, they commute with the isometries of (M, g)], e…
