Geometry and spectra of compact Riemann surfaces /

This classic 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 op...

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Bibliographic Details
Main Author: Buser, Peter
Corporate Author: SpringerLink (Online service)
Format: Printed Book
Language:English
Published: Heidelberg : Birkhauser, 2010.
Series:Modern Birkhäuser Classics
Subjects:
Algebra.
Differential equations, partial.
Geometry, algebraic.
Mathematics.
Algebraic Geometry.
Several Complex Variables and Analytic Spaces.
Online Access:http://www.columbia.edu/cgi-bin/cul/resolve?clio8629422
Table of Contents:
  • Preface.-Chapter 1: Hyperbolic Structures.-Chapter 2: Trigonometry
  • Chapter 3: Y-Pieces and Twist Parameters
  • Chapter 4:The Collar Theorem
  • Chapter 5: Bers' Constant and the Hairy Torus
  • Chapter 6: The Teichmüller Space
  • Chapter 7: The Spectrum of the Laplacian
  • Chapter 8: Small Eigenvalues
  • Chapter 9: Closed Geodesics and Huber's Theorem
  • Chapter 10: Wolpert's Theorem
  • Chapter 11: Sunada's Theorem
  • Chapter 12: Examples of Isospectral Riemann surfaces
  • Chapter 13: The Size of Isospectral Families
  • Chapter 14: Perturbations of the Laplacian in Hilbert Space.-Appendix: Curves and Isotopies.-Bibliography.-Index.-Glossary.

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