## Fundamentals of Hyperbolic Manifolds: Selected Expositions (Google eBook)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

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 |

### Common terms and phrases

angle assume basepoint bending lamination bending line Bonahon boundary components bounded Chabauty topology classical lipschitz constant closed geodesic closed subset compact subset conjecture contained continuous convex core convex hull convex hull boundary Corollary cosh curve cusp define Definition denote derivative developing map disjoint distance earthquake map endpoints equal euclidean exists Finite laminations finite number fixed point flat piece foliation follows function geodesic lamination geometrically finite given gluing edge half space Hausdorff homeomorphism homotopy horoball hyperbolic 3-manifolds hyperbolic plane hyperbolic structure incompressible induced inequality infinity injectivity radius intersection interval intrinsic metric Kleinian groups left earthquake Lemma I1 length limit lipschitz constant Math measured laminations nearest point retraction neighbourhood Note orientation orthogonal pleating locus Poincare metric proof Proposition prove rectifiable path relative compact core result Riemannian manifold Section sequence simply connected sinh Sullivan support plane Suppose Thurston transverse transverse measure triangle vector field zero