Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Topics in Spectral Geometry
 
Michael Levitin University of Reading, Reading, United Kingdom
Dan Mangoubi The Hebrew University, Jerusalem, Israel
Iosif Polterovich Université de Montréal, Montréal, QC, Canada
Softcover ISBN:  978-1-4704-7548-2
Product Code:  GSM/237.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7549-9
Product Code:  GSM/237.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7548-2
eBook: ISBN:  978-1-4704-7549-9
Product Code:  GSM/237.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
Click above image for expanded view
Topics in Spectral Geometry
Michael Levitin University of Reading, Reading, United Kingdom
Dan Mangoubi The Hebrew University, Jerusalem, Israel
Iosif Polterovich Université de Montréal, Montréal, QC, Canada
Softcover ISBN:  978-1-4704-7548-2
Product Code:  GSM/237.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7549-9
Product Code:  GSM/237.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7548-2
eBook ISBN:  978-1-4704-7549-9
Product Code:  GSM/237.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 2372023; 325 pp
    MSC: Primary 35; Secondary 47; 58; 65

    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.

    Readership

    Graduate students and researchers interested in differential geometry and Laplace operators.

  • Table of Contents
     
     
    • Chapters
    • Strings, drums, and the Laplacian
    • The spectral theorems
    • Variational principles and applications
    • Nodal geometry of eigenfunctions
    • Eigenvalue inequalities
    • Heat equation, spectral invariants, and isospectrality
    • The Steklov problem and the Dirichlet-to-Neumann map
    • A short tutorial on numerical spectral geometry
    • Background definitions and notation
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Accessibility – to request an alternate format of an AMS title
Volume: 2372023; 325 pp
MSC: Primary 35; Secondary 47; 58; 65

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.

Readership

Graduate students and researchers interested in differential geometry and Laplace operators.

  • Chapters
  • Strings, drums, and the Laplacian
  • The spectral theorems
  • Variational principles and applications
  • Nodal geometry of eigenfunctions
  • Eigenvalue inequalities
  • Heat equation, spectral invariants, and isospectrality
  • The Steklov problem and the Dirichlet-to-Neumann map
  • A short tutorial on numerical spectral geometry
  • Background definitions and notation
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
You may be interested in...
Please select which format for which you are requesting permissions.