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Spectral Geometry of the Laplacian: Spectral Analysis and Differential Geometry of the Laplacian
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Bibliographic Detail
Publisher World Scientific Pub Co Inc
Publication date November 30, 2016
Pages 350
Binding Hardcover
Book category Adult Non-Fiction
ISBN-13 9789813109087
ISBN-10 9813109084
Original list price $98.00
Summaries and Reviews description: Product Description: 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.

Readership: Researchers in differential geometry and partial differential equations.

Book cover for 9789813109087
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from World Scientific Pub Co Inc (November 30, 2016)
9789813109087 | details & prices | 350 pages | List price $98.00
About: The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is called the spectrum.

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