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

Released on by Hajime Urakawa
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  • Spectral Geometry of the Laplacian: Spectral Analysis and Differential Geometry of the Laplacian Book Detail

  • Author : Hajime Urakawa
  • Release Date : 2017
  • Publisher : World Scientific Publishing Company
  • Genre : Mathematics
  • Pages : 350
  • ISBN 13 : 9789813109087
  • File Size : 67,67 MB
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Spectral Geometry of the Laplacian: Spectral Analysis and Differential Geometry of the Laplacian by Hajime Urakawa PDF Summary

Book 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 Verdier, 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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Topics in Spectral Geometry

Topics in Spectral Geometry

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