Ebook Download 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
Ebook Download Spectral Geometry of the Laplacian: Spectral Analysis and Differential Geometry of the Laplacian
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From the Inside Flap
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 LichnerowiczObata's theorem on the first eigenvalue, the Cheng's estimates of the kth eigenvalues, and PaynePolyaWeinberger'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.
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Product details
Hardcover: 312 pages
Publisher: World Scientific Publishing Company (August 2, 2017)
Language: English
ISBN-10: 9789813109087
ISBN-13: 978-9813109087
ASIN: 9813109084
Product Dimensions:
5.9 x 0.9 x 9.1 inches
Shipping Weight: 1.3 pounds (View shipping rates and policies)
Average Customer Review:
5.0 out of 5 stars
1 customer review
Amazon Best Sellers Rank:
#2,049,600 in Books (See Top 100 in Books)
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