Geometry and Spectra of Compact Riemann Surfaces

• Main Author: Buser, Peter. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Boston : Birkhũser Boston, 2010.
• Series: Modern Birkhũser Classics
• Subjects: Mathematics.; Algebra.; Geometry, algebraic.; Differential equations, partial.; Several Complex Variables and Analytic Spaces.; Algebraic Geometry.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-8176-4992-0

This classic monograph is a self-contained introduction to the geometry of Riemann surfaces of constant curvature <U+0013>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 t...

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<U+0019> Constant and the Hairy Torus
• Chapter 6: The Teichm<U+00fc>ller Space
• Chapter 7: The Spectrum of the Laplacian
• Chapter 8: Small Eigenvalues
• Chapter 9: Closed Geodesics and Huber<U+0019>s Theorem
• Chapter 10: Wolpert<U+0019>s Theorem
• Chapter 11: Sunada<U+0019>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.