Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Spectral Geometry of the Laplacian: Spectral Analysis and Differential Geometry of the Laplacian

Spectral Geometry of the Laplacian: Spectral Analysis and Differential Geometry of the Laplacian

Urakawa, Hajime

Hardcover

General MathematicsGeneral ScienceGeometry

ISBN10: 9813109084
ISBN13: 9789813109087
Publisher: World Scientific Publishing Company
Published: Aug 2 2017
Pages: 312
Weight: 1.30
Height: 0.90 Width: 5.90 Depth: 9.10
Language: English

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.

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