The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is named 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 1st eigenvalue, the Lichnerowicz–Obata's theorem at the first eigenvalue, the Cheng's estimates of the kth eigenvalues, and Payne–Pólya–Weinberger's inequality of the Dirichlet eigenvalue of the Laplacian also are defined.
- Topological and Uniform Spaces (Undergraduate Texts in Mathematics)
- Basic Hypergeometric Series (Encyclopedia of Mathematics and its Applications)
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- Geometry VI: Riemannian Geometry: Volume 91 (Encyclopaedia of Mathematical Sciences)
- Metric and Differential Geometry: The Jeff Cheeger Anniversary Volume: 297 (Progress in Mathematics)
Extra info for Projektive Geometrie der Ebene Unter Benutzung der Punktrechnung Dargestellt: Erster Band: Binäres: 1 (German Edition)
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