Fundamentals of Hyperbolic Manifolds
Selected Expositions

Reissued articles from two classic sources on hyperbolic manifolds with new sections describing recent work.

R. D. Canary (Edited by), A. Marden (Edited by), D. B. A. Epstein (Edited by)

9780521615587, Cambridge University Press

Paperback, published 13 April 2006

348 pages, 75 b/w illus.
22.7 x 15.2 x 1.8 cm, 0.492 kg

'The book covers the basic properties, and explains the mathematical framework for understanding the 3-dimensional spaces that support a hyperbolic metric.' L'enseignement mathematique

Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.

Preface 2005
Preface
Part I. Notes on Notes of Thurston R. D. Canary, D. B. A. Epstein and P. Green
Part II. Convex Hulls in Hyperbolic Space, a Theorem of Sullivan, and Measured Pleated Surfaces D. B. A. Epstein and A. Marden
Part III. Earthquakes in Two-Dimensional Hyperbolic Geometry William P. Thurston
Part IV. Lectures on Measures on Limit Sets of Kleinian Groups S. J. Patterson.

Subject Areas: Analytic topology [PBPH], Analytic geometry [PBMS], Complex analysis, complex variables [PBKD]