"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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Bibliographische Detailangaben

1. Verfasser:	Urakawa, Hajime 1946- (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Singapore World Scientific © 2017
Schlagworte:	Symmetric matrices Eigenvalues Spectral geometry Riemannian manifolds Electronic books Spektralgeometrie Laplace-Operator
Online-Zugang:	BTU01 FHN01 Volltext
Zusammenfassung:	"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
Beschreibung:	Title from PDF title page (viewed July 27, 2017)
Beschreibung:	1 Online-Ressource (xii, 297 Seiten) Diagramme
ISBN:	9789813109094
DOI:	10.1142/10018