World Scientific Publishing Company
Spectral Geometry of the Laplacian: Spectral Analysis and Differential Geometry of the Laplacian
Product Code:
9789813109087
ISBN13:
9789813109087
Condition:
New
$125.22
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 Verdier, 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.
| Author: Hajime Urakawa |
| Publisher: World Scientific Publishing Company |
| Publication Date: Aug 02, 2017 |
| Number of Pages: 350 pages |
| Language: English |
| Binding: Hardcover |
| ISBN-10: 9813109084 |
| ISBN-13: 9789813109087 |
Spectral Geometry of the Laplacian: Spectral Analysis and Differential Geometry of the Laplacian
$125.22
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 Verdier, 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.
| Author: Hajime Urakawa |
| Publisher: World Scientific Publishing Company |
| Publication Date: Aug 02, 2017 |
| Number of Pages: 350 pages |
| Language: English |
| Binding: Hardcover |
| ISBN-10: 9813109084 |
| ISBN-13: 9789813109087 |
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