Volume 12, issue 1 (2008)

Download this article
For screen
For printing
Recent Issues

Volume 17 (2013)
Issue 1 1–620
Issue 2 621–

Volume 16 (2012) 1–4

Volume 15 (2011) 1–4

Volume 14 (2010) 1–5

Volume 13 (2009) 1–5

Volume 12 (2008) 1–5

Volume 11 (2007)

Volume 10 (2006)

Volume 9 (2005)

Volume 8 (2004)

Volume 7 (2003)

Volume 6 (2002)

Volume 5 (2001)

Volume 4 (2000)

Volume 3 (1999)

Volume 2 (1998)

Volume 1 (1997)

G&T Monographs
The Journal
About the Journal
Editorial Board
Editorial Interests
Author Index
Editorial procedure
Submission Guidelines
Submission Page
Author copyright form
Subscriptions
Contacts
G&T Publications
GTP Author Index

Projective structures, grafting and measured laminations

David Dumas and Michael Wolf

Geometry and Topology 12 (2008) 351–386

DOI: 10.2140/gt.2008.12.351

Bibliography
1 L Bers, Simultaneous uniformization, Bull. Amer. Math. Soc. 66 (1960) 94–97 MR0111834
2 L Bers, Correction to “Spaces of Riemann surfaces as bounded domains”, Bull. Amer. Math. Soc. 67 (1961) 465–466 MR0130972
3 F Bonahon, Earthquakes on Riemann surfaces and on measured geodesic laminations, Trans. Amer. Math. Soc. 330 (1992) 69–95 MR1049611
4 F Bonahon, Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form, Ann. Fac. Sci. Toulouse Math. (6) 5 (1996) 233–297 MR1413855
5 F Bonahon, Geodesic laminations with transverse Hölder distributions, Ann. Sci. École Norm. Sup. (4) 30 (1997) 205–240 MR1432054
6 F Bonahon, Transverse Hölder distributions for geodesic laminations, Topology 36 (1997) 103–122 MR1410466
7 F Bonahon, Variations of the boundary geometry of 3–dimensional hyperbolic convex cores, J. Differential Geom. 50 (1998) 1–24 MR1678469
8 F Bonahon, Kleinian groups which are almost Fuchsian, J. Reine Angew. Math. 587 (2005) 1–15 MR2186972
9 F Bonahon, J P Otal, Laminations measurées de plissage des variétés hyperboliques de dimension 3, Ann. of Math. (2) 160 (2004) 1013–1055 MR2144972
10 R Díaz, I Kim, Asymptotic behavior of grafting rays (2007) Preprint
11 D Dumas, Grafting, pruning, and the antipodal map on measured laminations, J. Differential Geom. 74 (2006) 93–118 MR2260929 \em Erratum, J. Differential Geom. 77 (2007) 175–176
12 D Dumas, The Schwarzian derivative and measured laminations on Riemann surfaces, Duke Math. J. 140 (2007) 203–243 MR2359819
13 D B A Epstein, A Marden, Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces, from: "Analytical and geometric aspects of hyperbolic space (Coventry/Durham, 1984)", London Math. Soc. Lecture Note Ser. 111, Cambridge Univ. Press (1987) 113–253 MR903852
14 D B A Epstein, A Marden, V Markovic, Quasiconformal homeomorphisms and the convex hull boundary, Ann. of Math. (2) 159 (2004) 305–336 MR2052356
15 D Gallo, M Kapovich, A Marden, The monodromy groups of Schwarzian equations on closed Riemann surfaces, Ann. of Math. (2) 151 (2000) 625–704 MR1765706
16 F P Gardiner, Teichmüller theory and quadratic differentials, Pure and Applied Mathematics (New York), John Wiley & Sons (1987) MR903027 A Wiley–Interscience Publication
17 F P Gardiner, H Masur, Extremal length geometry of Teichmüller space, Complex Variables Theory Appl. 16 (1991) 209–237 MR1099913
18 W M Goldman, Projective structures with Fuchsian holonomy, J. Differential Geom. 25 (1987) 297–326 MR882826
19 D A Hejhal, Monodromy groups and linearly polymorphic functions, Acta Math. 135 (1975) 1–55 MR0463429
20 Y Kamishima, S P Tan, Deformation spaces on geometric structures, from: "Aspects of low-dimensional manifolds", Adv. Stud. Pure Math. 20, Kinokuniya (1992) 263–299 MR1208313
21 A B Katok, Invariant measures of flows on orientable surfaces, Dokl. Akad. Nauk SSSR 211 (1973) 775–778 MR0331438
22 S P Kerckhoff, The asymptotic geometry of Teichmüller space, Topology 19 (1980) 23–41 MR559474
23 S P Kerckhoff, Earthquakes are analytic, Comment. Math. Helv. 60 (1985) 17–30 MR787659
24 S P Kerckhoff, Simplicial systems for interval exchange maps and measured foliations, Ergodic Theory Dynam. Systems 5 (1985) 257–271 MR796753
25 F Klein, Vorlesungen über die Hypergeometrische funktion, Springer–Verlag, Berlin (1933)
26 G Levitt, Feuilletages des surfaces, Ann. Inst. Fourier (Grenoble) 32 (1982) 179–217 MR662443
27 B Maskit, On a class of Kleinian groups, Ann. Acad. Sci. Fenn. Ser. A I No. 442 (1969) MR0252638
28 H Masur, Interval exchange transformations and measured foliations, Ann. of Math. (2) 115 (1982) 169–200 MR644018
29 C T McMullen, Complex earthquakes and Teichmüller theory, J. Amer. Math. Soc. 11 (1998) 283–320 MR1478844
30 S Nag, The complex analytic theory of Teichmüller spaces, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons (1988) MR927291 A Wiley-Interscience Publication.
31 J P Otal, Le théorème d'hyperbolisation pour les variétés fibrées de dimension 3, Astérisque (1996) MR1402300
32 A Papadopoulos, Deux remarques sur la géométrie symplectique de l'espace des feuilletages mesurés sur une surface, Ann. Inst. Fourier (Grenoble) 36 (1986) 127–141 MR850748
33 R C Penner, J L Harer, Combinatorics of train tracks, Annals of Mathematics Studies 125, Princeton University Press (1992) MR1144770
34 I D Platis, Complex symplectic geometry of quasi-Fuchsian space, Geom. Dedicata 87 (2001) 17–34 MR1866841
35 M Rees, An alternative approach to the ergodic theory of measured foliations on surfaces, Ergodic Theory Dynamical Systems 1 (1981) 461–488 MR662738
36 K P Scannell, M Wolf, The grafting map of Teichmüller space, J. Amer. Math. Soc. 15 (2002) 893–927 MR1915822
37 C Series, On Kerckhoff minima and pleating loci for quasi-Fuchsian groups, Geom. Dedicata 88 (2001) 211–237 MR1877217
38 C Series, Limits of quasi-Fuchsian groups with small bending, Duke Math. J. 128 (2005) 285–329 MR2140265
39 C Series, Thurston's bending measure conjecture for once punctured torus groups, from: "Spaces of Kleinian groups", London Math. Soc. Lecture Note Ser. 329, Cambridge Univ. Press (2006) 75–89 MR2258745
40 Y Sözen, F Bonahon, The Weil–Petersson and Thurston symplectic forms, Duke Math. J. 108 (2001) 581–597 MR1838662
41 D Sullivan, W Thurston, Manifolds with canonical coordinate charts: some examples, Enseign. Math. (2) 29 (1983) 15–25 MR702731
42 H Tanigawa, Grafting, harmonic maps and projective structures on surfaces, J. Differential Geom. 47 (1997) 399–419 MR1617652
43 W P Thurston, Geometry and Topology of Three-Manifolds (1979)
44 W P Thurston, Earthquakes in two-dimensional hyperbolic geometry, from: "Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984)", London Math. Soc. Lecture Note Ser. 112, Cambridge Univ. Press (1986) 91–112 MR903860
45 W P Thurston, Minimal stretch maps between hyperbolic surfaces arXiv:math.GT/9801039
46 A J Tromba, Teichmüller theory in Riemannian geometry, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag (1992) MR1164870 Lecture notes prepared by Jochen Denzler.
47 W A Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math. (2) 115 (1982) 201–242 MR644019
48 S Wolpert, An elementary formula for the Fenchel–Nielsen twist, Comment. Math. Helv. 56 (1981) 132–135 MR615620
49 S Wolpert, The Fenchel–Nielsen deformation, Ann. of Math. (2) 115 (1982) 501–528 MR657237
50 S Wolpert, On the symplectic geometry of deformations of a hyperbolic surface, Ann. of Math. (2) 117 (1983) 207–234 MR690844
51 S Wolpert, Chern forms and the Riemann tensor for the moduli space of curves, Invent. Math. 85 (1986) 119–145 MR842050
52 P G Zograf, L A Takhtadzhyan, On the Liouville equation, accessory parameters and the geometry of Teichmüller space for Riemann surfaces of genus 0, Mat. Sb. (N.S.) 132(174) (1987) 147–166 MR882831