Introduction to Hyperbolic Geometry

The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics. Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincaré disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications.

Authors: Borthwick, David
Provides an accessible introduction to geometric scattering theory and the theory of resonances
Discusses important developments such as resonance counting, analysis of the Selberg zeta function, and the Poisson formula
New chapters cover resolvent estimates, wave propagation, and Naud’s proof of a spectral gap for convex hyperbolic surfaces
Makes use of new techniques for resonance plotting that more clearly illustrate existing results of resonance distribution