Topics in Spectral Geometry (Graduate Studies in Mathematics, 237) - Softcover

Michael Levitin; Dan Mangoubi; Iosif Polterovich

Softcover

ISBN 10: 1470475480 ISBN 13: 9781470475482

Publisher: American Mathematical Society, 2023

Synopsis

It is remarkable that various distinct physical phenomena, such as wave propagation, heat diffusion, electron movement in quantum mechanics, oscillations of fluid in a container, can be described using the same differential operator, the Laplacian. Spectral data (i.e., eigenvalues and eigenfunctions) of the Laplacian depend in a subtle way on the geometry of the underlying object, e.g., a Euclidean domain or a Riemannian manifold, on which the operator is defined. This dependence, or, rather, the interplay between the geometry and the spectrum, is the main subject of spectral geometry. Its roots can be traced to Ernst Chladni's experiments with vibrating plates, Lord Rayleigh's theory of sound, and Mark Kac's celebrated question “Can one hear the shape of a drum?” In the second half of the twentieth century spectral geometry emerged as a separate branch of geometric analysis. Nowadays it is a rapidly developing area of mathematics, with close connections to other fields, such as differential geometry, mathematical physics, partial differential equations, number theory, dynamical systems, and numerical analysis. This book can be used for a graduate or an advanced undergraduate course on spectral geometry, starting from the basics but at the same time covering some of the exciting recent developments which can be explained without too many prerequisites.

About this title

About the Author

Michael Levitin, University of Reading, United Kingdom, Dan Mangoubi, The Hebrew University, Jerusalem, Israel, and Iosif Polterovich, Université de Montréal, QC, Canada

Edition details

• Publisher: American Mathematical Society
• Publication date: 2023
• Language: English
• ISBN 10: 1470475480
• ISBN 13: 9781470475482
• Binding: Paperback
• Number of pages: 325