ENGLISH

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

By Hajime Urakawa

Book information

Publisher
World Scientific
Year
2017
ISBN
9813109084, 9789813109087
Language
english
Format
PDF
Filesize
2 MB (2369311 bytes)
Pages
312\310
Time added
2018-03-07 07:23:53
Differential Equations;Applied;Mathematics;ScienceUsed & Rental Textbooks;Specialty Boutique

Description

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. Readership: Researchers in differential geometry and partial differential equations.

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