Buser Geometry and Spectra of Compact Riemann Surfaces

1. Auflage 2010
ISBN: 978-0-8176-4992-0
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 456 Seiten, Web PDF

Reihe: Modern Birkhäuser Classics

This monograph is a self-contained introduction to the geometry of Riemann Surfaces of constant curvature -1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.

Zielgruppe

Graduate

Autoren/Hrsg.

Buser, Peter

Inhaltsverzeichnis

Hyperbolic Structures.- Trigonometry.- Y-Pieces and Twist Parameters.- The Collar Theorem.- Bers’ Constant and the Hairy Torus.- The Teichmüller Space.- The Spectrum of the Laplacian.- Small Eigenvalues.- Closed Geodesics and Huber’s Theorem.- Wolpert’s Theorem.- Sunada’s Theorem.- Examples of Isospectral Riemann Surfaces.- The Size of Isospectral Families.- Perturbations of the Laplacian in Teichmüller Space.