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.
- Differential Geometry of Singular Spaces and Reduction of Symmetry (New Mathematical Monographs)
- Novikov Conjectures, Index Theorems, and Rigidity: Volume 1: Oberwolfach 1993 (London Mathematical Society Lecture Note Series)
- Das Glück, Mathematiker zu sein: Friedrich Hirzebruch und seine Zeit (German Edition)
- Algebraic Geometry over the Complex Numbers (Universitext)
Extra resources for An Axiomatic Approach to Geometry: Geometric Trilogy I
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