Spectral Geometry Of The Laplacian: Spectral Analysis And Differential Geometry Of The Laplacian
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€110.99
A01=Hajime Urakawa
Author_Hajime Urakawa
Category=PBMP
Eigenfunction
Eigenvalue
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Laplacian
Spectrum
Product details
- ISBN 9789813109087
- Publication Date: 02 Aug 2017
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
