The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is termed 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.
- Elliptic Curves (Graduate Texts in Mathematics)
- Manifolds, Tensors, and Forms: An Introduction for Mathematicians and Physicists
- Leibniz on the Parallel Postulate and the Foundations of Geometry: The Unpublished Manuscripts (Science Networks. Historical Studies)
- Theory of Transformation Groups I: General Properties of Continuous Transformation Groups. A Contemporary Approach and Translation
Extra info for A Fête of Topology: Papers Dedicated to Itiro Tamura
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