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.
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Zielgruppe
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ISBN-13
978-1-139-10698-6 (9781139106986)
Schweitzer Klassifikation
Herausgeber*in
University of Michigan, Ann Arbor
Richard Canary is a Professor of Mathematics at the University of Michigan.
University of Minnesota
Albert Marden is a Professor of Mathematics at the University of Minnesota.
University of Warwick
David Epstein is an Emeritus Professor at the University of Warwick.
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.
