Fundamentals of Hyperbolic Manifolds: Selected Expositions (Google eBook)

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R. D. Canary, A. Marden, D. B. A. Epstein
Cambridge University Press, Apr 13, 2006 - Mathematics
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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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Contents

Canary D B A Epstein P L Green
3
1 G Xstructures
31
2 Hyperbolic structures
49
3 Spaces of hyberbolic manifolds
59
4 Laminations
76
5 Pleated surfaces
89
CONVEX HULLS IN HYPERBOLIC SPACE
117
14 Convergence of laminations
150
Addendum 2005
255
EARTHQUAKES IN 2DIMENSIONAL
267
3 Associating earthquakes to maps of the circle
276
5 Earthquakes on hyperbolic surfaces
283
LECTURES ON MEASURES ON LIMIT SETS
291
2 A measure on the limit set
300
3 First fruits
308
4 Spectral theory
314

14 Themapp
197
Chapter I1 3 Measured pleated surfaces
211
Appendix
239
5 Geodesic flows
321
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About the author (2006)

Richard Canary is a Professor of Mathematics at the University of Michigan.

Albert Marden is a Professor of Mathematics at the University of Minnesota.

David Epstein is an Emeritus Professor at the University of Warwick.

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