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.
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SPECTRAL GEOMETRY OF THE LAPLACIAN: Spectral Analysis and Differential Geometry of the Laplacian
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.
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SPECTRAL GEOMETRY OF THE LAPLACIAN: Spectral Analysis and Differential Geometry of the Laplacian
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SPECTRAL GEOMETRY OF THE LAPLACIAN: Spectral Analysis and Differential Geometry of the Laplacian
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Product Details
| ISBN-13: | 9789813109100 |
|---|---|
| Publisher: | World Scientific Publishing Company, Incorporated |
| Publication date: | 06/02/2017 |
| Series: | Ltcc Advanced Mathematics Series , #5 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| Pages: | 312 |
| File size: | 23 MB |
| Note: | This product may take a few minutes to download. |
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