The Spectrum of Hyperbolic Surfaces

The Spectrum of Hyperbolic Surfaces
Author :
Publisher : Springer
Total Pages : 370
Release :
ISBN-10 : 3319276646
ISBN-13 : 9783319276649
Rating : 4/5 (649 Downloads)

Book Synopsis The Spectrum of Hyperbolic Surfaces by : Nicolas Bergeron

Download or read book The Spectrum of Hyperbolic Surfaces written by Nicolas Bergeron and published by Springer. This book was released on 2016-03-02 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called “arithmetic hyperbolic surfaces”, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them. After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss. The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.


The Spectrum of Hyperbolic Surfaces Related Books

The Spectrum of Hyperbolic Surfaces
Language: en
Pages: 370
Authors: Nicolas Bergeron
Categories: Mathematics
Type: BOOK - Published: 2016-03-02 - Publisher: Springer

DOWNLOAD EBOOK

This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called “arithm
Le spectre des surfaces hyperboliques
Language: fr
Pages: 350
Authors: Nicolas Bergeron
Categories: Mathematics
Type: BOOK - Published: 2011 - Publisher: Harlequin

DOWNLOAD EBOOK

This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called ĺlarithm
Spectral Theory of Infinite-Area Hyperbolic Surfaces
Language: en
Pages: 471
Authors: David Borthwick
Categories: Mathematics
Type: BOOK - Published: 2016-07-12 - Publisher: Birkhäuser

DOWNLOAD EBOOK

This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developmen
Geometry and Spectra of Compact Riemann Surfaces
Language: en
Pages: 473
Authors: Peter Buser
Categories: Mathematics
Type: BOOK - Published: 2010-10-29 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This monograph is a self-contained introduction to the geometry of Riemann Surfaces of constant curvature –1 and their length and eigenvalue spectra. It focus
Hyperbolic Metamaterials
Language: en
Pages: 81
Authors: Igor I Smolyaninov
Categories: Technology & Engineering
Type: BOOK - Published: 2018-03-23 - Publisher: Morgan & Claypool Publishers

DOWNLOAD EBOOK

Hyperbolic metamaterials were originally introduced to overcome the diffraction limit of optical imaging. Soon thereafter it was realized that hyperbolic metama