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OverviewThis work presents results and techniques concerning the spectral geometry corresponding to the Laplace-Beltrami operator and the Hodge-de Rham operators. It treats many topics that are not usually dealt with in this field, such as the continuous dependence of the eigenvalues with respect to the Riemannian metric in the C-topology, and some of their consequences, such as Uhlenbeck's genericity theorem; examples of non-isometric flat tori in all dimensions greater than or equal to four; Gordon's classical technique for constructing isospectral closed Riemannian manifolds; a detailed presentation of Sunada's technique and Pesce's approach to isospectrality; Gordon and Webb's example of non-isometric convex domains in Rn (n>=4) that are isospectral for both Dirichlet and Neumann boundary conditions; the Chanillo-Treves estimate for the first positive eigenvalue of the Hodge-de Rham operator, and more. Significant applications are developed, and many open problems, references and suggestions for further reading are given. Several themes for additional research are pointed out. Full Product DetailsAuthor: M.-E. Craioveanu , Mircea Puta , Themistocles RASSIASPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 2001 ed. Volume: 534 Dimensions: Width: 15.50cm , Height: 2.50cm , Length: 23.50cm Weight: 1.810kg ISBN: 9781402000522ISBN 10: 1402000529 Pages: 446 Publication Date: 31 October 2001 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents1. Introduction to Riemannian Manifolds.- 2. Canonical Differential Operators Associated to a Riemannian Manifold.- 3. Spectral Properties of the Laplace-Beltrami Operator and Applications.- 4. Isospectral Closed Riemannian Manifolds.- 5. Spectral Properties of the Laplacians for the de Rham Complex.- 6. Applications to Geometry and Topology.- 7. An Introduction to Witten-Helffer-Sjöstrand Theory.- 8. Open Problems and Comments.- 1. Review of Matrix Algebra.- 2. Eigenvectors and Eigenvalues.- 3. Diagonalizable Matrices. Triangularizable Matrices. Jordan Canonical Form.- 4. Eigenvalues and Eigenvectors of Real Symmetric and Hermitian Matrices.- References.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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