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Fundamentals of Hyperbolic Manifolds : Selected Expositions.

Author: R D Canary; A Marden; D B A Epstein
Publisher: Cambridge : Cambridge University Press, 2006.
Series: London Mathematical Society Lecture Note Series, 328.
Edition/Format:   eBook : Document : English
Database:WorldCat
Summary:
Reissued articles from two classic sources on hyperbolic manifolds with new sections describing recent work.
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Genre/Form: Electronic books
Congresses
Additional Physical Format: Print version:
Canary, R.D.
Fundamentals of Hyperbolic Manifolds : Selected Expositions.
Cambridge : Cambridge University Press, ©2006
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: R D Canary; A Marden; D B A Epstein
ISBN: 9781139116275 1139116274
OCLC Number: 769341705
Notes: III. 1.6. The measure and cause of earthquakes.
Description: 1 online resource (349 pages).
Contents: Cover; Title; Copyright; Contents; Preface; Preface 2005; PART I: NOTES ON NOTES OF THURSTON; A New Foreword; Chapter I.1. (G, X)-structures; I.1.1. (G, X)-structures on a manifold; I.1.2. Developing map and holonomy; I.1.3. Convexity; I.1.4. The developing map and convexity; I.1.5. The deformation space; I.1.6. Thickenings; I.1.7. Varying the structure; Chapter I.2. Hyperbolic structures; I.2.1. Möbius groups; I.2.2. The thick-thin decomposition; I.2.3. The nearest point retraction; I.2.4. Neighbourhoods of convex hyperbolic manifolds; I.2.5. Convex thickenings. Chapter I.3. Spaces of hyberbolic manifoldsI. 3.1. The geometric topology; I.3.2. e-relations and approximate isometries; Chapter I.4. Laminations; I.4.1. Geodesic laminations; I.4.2. Minimal laminations; Chapter I.5. Pleated surfaces; I.5.1. Introduction; I.5.2. Compactness properties of pleated surfaces; I.5.3. Realizations; PART II: CONVEX HULLS IN HYPERBOLIC SPACE, A THEOREM OF SULLIVAN, AND MEASURED PLEATED SURFACES; Chapter II. 1. Convex hulls; II. 1.1. Introduction; II. 1.2. Hyperbolic convex hulls; II. 1.3. The nearest point retraction; II. 1.4. Properties of hyperbolic convex hulls. II. 1.5. Metric on convex hull boundaryII. 1.6. Hyperbolic convex hulls; II. 1.7. Limits of lines and planes; II. 1.8. Ridge lines; II. 1.9. The roof; II. 1.10. Lowering the roof; II. 1.11. The bending measure; II. 1.12. The boundary is a complete hyperbolic manifold; II. 1.13. Finite approximations to the convex hull boundary; II. 1.14. Convergence of laminations; Chapter II. 2. Foliations and the epsilon distant surface; II. 2.1. Introduction; II. 2.2. The epsilon distant surface; II. 2.3. From infinity to the epsilon surface; II. 2.4. Extending a lamination to a pair of orthogonal foliations. II. 2.5. Some standard vector fieldsII. 2.6. Lipschitz line fields in the hyperbolic plane; II. 2.7. Foliation coordinates; II. 2.8. Formulas in the hyperbolic plane; II. 2.9. Flat equidistant surfaces; II. 2.10. Foliations on the convex hull; II. 2.11. Three orthogonal fields; II. 2.12. The equidistant surface from a finitely bent convex hull boundary; II. 2.13. Surfaces equidistant from a general convex hull boundary; II. 2.14. The map?; II. 2.15. Numerical results; II. 2.16. Counterexample; Chapter II. 3. Measured pleated surfaces; II. 3.1. Introduction; II. 3.2. Finite quakebends; II. 3.3. Norms. II. 3.4. Products of rotations about geodesicsII. 3.5. The quakebend cocycle; II. 3.6. The quakebend map; II. 3.7. Invariance; II. 3.8. Deformations; II. 3.9. Derivatives; II. 3.10. Second variation; II. 3.11. Varying the lamination; Appendix; Addendum 2005; PART III: EARTHQUAKES IN 2-DIMENSIONAL HYPERBOLIC GEOMETRY; Chapter III. 1. Earthquakes in 2-dimensional hyperbolic geometry; III. 1.1. Introduction; III. 1.2. What are hyperbolic earthquakes?; III. 1.3. Associating earthquakes to maps of the circle; III. 1.4. Examples; III. 1.5. Earthquakes on hyperbolic surfaces.
Series Title: London Mathematical Society Lecture Note Series, 328.

Abstract:

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

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