Articles liés à Spectral Geometry of the Laplacian: Spectral Analysis...

Spectral Geometry of the Laplacian: Spectral Analysis and Differential Geometry of the Laplacian - Couverture rigide

Urakawa, Hajime

 
9789813109087: Spectral Geometry of the Laplacian: Spectral Analysis and Differential Geometry of the Laplacian
Couverture rigide
ISBN 10 : 9813109084 ISBN 13 : 9789813109087
Editeur : World Scientific Publishing Co Pte Ltd, 2017

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
World Scientific Publishing Co Pte Ltd
Date d'édition
2017
Langue
anglais
ISBN 10 
9813109084
ISBN 13 
9789813109087
Reliure
Relié
Numéro d'édition
1
Nombre de pages
310
Coordonnées du fabricant
non disponible
Personne responsable
gpsr@libri.de
gpsr@libri.de

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