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
Author: Hajime Urakawa
language: en
Publisher: World Scientific Publishing Company
Release Date: 2017
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.
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.
The Laplacian on a Riemannian Manifold
Author: Steven Rosenberg
language: en
Publisher: Cambridge University Press
Release Date: 1997-01-09
This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.