"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–...

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Bibliographic Details

Main Author:	Urakawa, Hajime 1946- (Author)
Format:	Electronic eBook
Language:	English
Published:	Singapore World Scientific © 2017
Subjects:	Symmetric matrices Eigenvalues Spectral geometry Riemannian manifolds Electronic books Spektralgeometrie Laplace-Operator
Online Access:	BTU01 FHN01 Volltext
Summary:	"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–Weinberger's inequality of the Dirichlet eigenvalue of the Laplacian are also described. Then, the theorem of Colin de Verdière, that is, the spectrum determines the totality of all the lengths of closed geodesics is described. We give the V Guillemin and D Kazhdan's theorem which determines the Riemannian manifold of negative curvature."--Publisher's website
Item Description:	Title from PDF title page (viewed July 27, 2017)
Physical Description:	1 Online-Ressource (xii, 297 Seiten) Diagramme
ISBN:	9789813109094
DOI:	10.1142/10018