Old and New Aspects in Spectral Geometry (Hardcover, 2001 ed.)

This work presents some classical as well as some very recent 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 CINFINITY-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-TrA]ves estimate for the first positive eigenvalue of the Hodge-de Rham operator, etc. Significant applications are developed, and many open problems, references and suggestions for further reading are given. Several themes for additional research are pointed out. Audience: This volume is designed as an introductory text for mathematicians and physicists interested in global analysis, analysis on manifolds, differential geometry, linear and multilinear algebra, and matrix theory. It is accessible to readers whose background includes basic Riemannian geometry and functional analysis. These mathematical prerequisites are covered in the first two chapters, thus making the book largely self-contained.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Mathematics and Its Applications, 534
Release date:	October 2001
First published:	2001
Authors:	M.-E. Craioveanu • Mircea Puta • Themistocles Rassias
Dimensions:	235 x 155 x 31mm (L x W x T)
Format:	Hardcover
Pages:	446
Edition:	2001 ed.
ISBN-13:	978-1-4020-0052-2
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Books > Science & Mathematics > Mathematics > Topology > General Promotions
LSN:	1-4020-0052-9
Barcode:	9781402000522

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