Spectral Geometry of the Laplacian Spectral Analysis and Differential Geometry of the Laplacian is popular PDF and ePub book, written by Hajime Urakawa in 2017, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Spectral Geometry of the Laplacian Spectral Analysis and Differential Geometry of the Laplacian can be Read Online from any device for your convenience.
Spectral Geometry of the Laplacian Spectral Analysis and Differential Geometry of the Laplacian Book PDF Summary
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.
Detail Book of Spectral Geometry of the Laplacian Spectral Analysis and Differential Geometry of the Laplacian PDF
- Author : Hajime Urakawa
- Release : 21 September 2024
- Publisher : World Scientific Publishing Company
- ISBN : 9813109084
- Genre : Mathematics
- Total Page : 350 pages
- Language : English
- PDF File Size : 12,7 Mb
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