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The convex core of quasifuchsian manifolds with particles

Cyril Lecuire and Jean-Marc Schlenker

Geometry & Topology 18 (2014) 2309–2373
Bibliography
1 L Ahlfors, L Bers, Riemann's mapping theorem for variable metrics, Ann. of Math. 72 (1960) 385 MR0115006
2 A D Aleksandrov, V A Zalgaller, Intrinsic geometry of surfaces, Trans. Math. Monog. 15, Amer. Math. Soc. (1967) MR0216434
3 L Andersson, T Barbot, R Benedetti, F Bonsante, W M Goldman, F Labourie, K P Scannell, J M Schlenker, Notes on: “Lorentz spacetimes of constant curvature” by G Mess, Geom. Dedicata 126 (2007) 47 MR2328922
4 W Ballmann, M Gromov, V Schroeder, Manifolds of nonpositive curvature, Progress in Mathematics 61, Birkhäuser (1985) MR823981
5 T Barbot, F Bonsante, J M Schlenker, Collisions of particles in locally AdS spacetimes, I: Local description and global examples, Comm. Math. Phys. 308 (2011) 147 MR2842974
6 T Barbot, F Bonsante, J M Schlenker, Collisions of particles in locally AdS spacetimes, II: Moduli of globally hyperbolic spaces, Comm. Math. Phys. 327 (2014) 691 MR3192047
7 R Benedetti, C Petronio, Lectures on hyperbolic geometry, Springer, Berlin (1992) MR1219310
8 L Bers, Simultaneous uniformization, Bull. Amer. Math. Soc. 66 (1960) 94 MR0111834
9 A L Besse, Einstein manifolds, Ergeb. Math. Grenzgeb. 10, Springer, Berlin (1987) MR867684
10 M Boileau, B Leeb, J Porti, Geometrization of $3$–dimensional orbifolds, Ann. of Math. 162 (2005) 195 MR2178962
11 M Boileau, J Porti, Geometrization of $3$–orbifolds of cyclic type, Astérisque 272, Soc. Math. France (2001) 208 MR1844891
12 F Bonahon, J P Otal, Laminations measurées de plissage des variétés hyperboliques de dimension 3, Ann. of Math. 160 (2004) 1013 MR2144972
13 F Bonsante, J M Schlenker, AdS manifolds with particles and earthquakes on singular surfaces, Geom. Funct. Anal. 19 (2009) 41 MR2507219
14 F Bonsante, J M Schlenker, Fixed points of compositions of earthquakes, Duke Math. J. 161 (2012) 1011 MR2913100
15 M Bridgeman, Average bending of convex pleated planes in hyperbolic three-space, Invent. Math. 132 (1998) 381 MR1621436
16 M Bridgeman, R D Canary, From the boundary of the convex core to the conformal boundary, Geom. Dedicata 96 (2003) 211 MR1956842
17 J F Brock, R D Canary, Y N Minsky, The classification of Kleinian surface groups, II: The ending lamination conjecture, Ann. of Math. 176 (2012) 1 MR2925381
18 J F Brock, H Masur, Y N Minsky, Asymptotics of Weil–Petersson geodesic, I: Ending laminations, recurrence, and flows, Geom. Funct. Anal. 19 (2010) 1229 MR2585573
19 K Bromberg, Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives, J. Amer. Math. Soc. 17 (2004) 783 MR2083468
20 K Bromberg, Rigidity of geometrically finite hyperbolic cone-manifolds, Geom. Dedicata 105 (2004) 143 MR2057249
21 R Brooks, J P Matelski, Collars in Kleinian groups, Duke Math. J. 49 (1982) 163 MR650375
22 A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Math. Soc. Student Texts 9, Cambridge Univ. Press (1988) MR964685
23 D Cooper, C D Hodgson, S P Kerckhoff, Three-dimensional orbifolds and cone-manifolds, MSJ Memoirs 5, Math. Soc. Japan (2000) MR1778789
24 E B Dryden, H Parlier, Collars and partitions of hyperbolic cone-surfaces, Geom. Dedicata 127 (2007) 139 MR2338522
25 D Dumas, Complex projective structures, from: "Handbook of Teichmüller theory, Vol. II" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 13, Eur. Math. Soc., Zürich (2009) 455 MR2497780
26 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" (editor D B A Epstein), London Math. Soc. Lecture Note Ser. 111, Cambridge Univ. Press (1987) 113 MR903852
27 D B A Epstein, V Markovic, The logarithmic spiral: A counterexample to the $K=2$ conjecture, Ann. of Math. 161 (2005) 925 MR2153403
28 J L Harer, R C Penner, Combinatorics of train tracks, Annals of Mathematics Studies 125, Princeton Univ. Press (1992) MR1144770
29 C D Hodgson, S P Kerckhoff, Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery, J. Differential Geom. 48 (1998) 1 MR1622600
30 G ’t Hooft, The evolution of gravitating point particles in $2+1$ dimensions, Classical Quantum Gravity 10 (1993) 1023 MR1219446
31 G ’t Hooft, Quantization of point particles in $(2+1)$–dimensional gravity and spacetime discreteness, Classical Quantum Gravity 13 (1996) 1023 MR1390098
32 S P Kerckhoff, The Nielsen realization problem, Ann. of Math. 117 (1983) 235 MR690845
33 K Krasnov, J M Schlenker, On the renormalized volume of hyperbolic $3$–manifolds, Comm. Math. Phys. 279 (2008) 637 MR2386723
34 K Krasnov, J M Schlenker, A symplectic map between hyperbolic and complex Teichmüller theory, Duke Math. J. 150 (2009) 331 MR2569616
35 K Krasnov, J M Schlenker, The Weil–Petersson metric and the renormalized volume of hyperbolic $3$–manifolds, from: "Handbook of Teichmüller theory, Vol. III" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 17, Eur. Math. Soc., Zürich (2012) 779 MR2952776
36 R S Kulkarni, U Pinkall, A canonical metric for Möbius structures and its applications, Math. Z. 216 (1994) 89 MR1273468
37 F Labourie, Métriques prescrites sur le bord des variétés hyperboliques de dimension $3$, J. Differential Geom. 35 (1992) 609 MR1163450
38 C Lecuire, Plissage des variétés hyperboliques de dimension $3$, Invent. Math. 164 (2006) 85 MR2207784
39 C T McMullen, The moduli space of Riemann surfaces is Kähler hyperbolic, Ann. of Math. 151 (2000) 327 MR1745010
40 G Mess, Lorentz spacetimes of constant curvature, Geom. Dedicata 126 (2007) 3 MR2328921
41 R Meyerhoff, A lower bound for the volume of hyperbolic $3$–manifolds, Canad. J. Math. 39 (1987) 1038 MR918586
42 Y N Minsky, The classification of punctured-torus groups, Ann. of Math. 149 (1999) 559 MR1689341
43 S Moroianu, J M Schlenker, Quasi-Fuchsian manifolds with particles, J. Differential Geom. 83 (2009) 75 MR2545031
44 J P Otal, Le théorème d'hyperbolisation pour les variétés fibrées de dimension $3$, Astérisque 235, Soc. Math. France (1996) MR1402300
45 J M Schlenker, Métriques sur les polyèdres hyperboliques convexes, J. Differential Geom. 48 (1998) 323 MR1630178
46 J M Schlenker, Convex polyhedra in Lorentzian space-forms, Asian J. Math. 5 (2001) 327 MR1868937
47 J M Schlenker, Des immersions isométriques de surfaces aux variétés hyperboliques à bord convexe, Sémin. Théor. Spectr. Géom. 21, Univ. Grenoble I (2003) 165 MR2052831
48 J M Schlenker, Hyperbolic manifolds with convex boundary, Invent. Math. 163 (2006) 109 MR2208419
49 G Schumacher, S Trapani, Weil–Petersson geometry for families of hyperbolic conical Riemann surfaces, Michigan Math. J. 60 (2011) 3 MR2785861
50 M Spivak, A comprehensive introduction to differential geometry, Vol. III, Publish or Perish (1979)
51 L A Takhtajan, L P Teo, Liouville action and Weil–Petersson metric on deformation spaces, global Kleinian reciprocity and holography, Comm. Math. Phys. 239 (2003) 183 MR1997440
52 L A Takhtajan, P G Zograf, On the uniformization of Riemann surfaces and on the Weil–Petersson metric on the Teichmüller and Schottky spaces, Mat. Sb. 132(174) (1987) 304, 444 MR889594
53 L A Takhtajan, P G Zograf, Hyperbolic $2$–spheres with conical singularities, accessory parameters and Kähler metrics on $\mathscr{M} _{0,n}$, Trans. Amer. Math. Soc. 355 (2003) 1857 MR1953529
54 W P Thurston, The geometry and topology of $3$–manifolds, lecture notes, Princeton University (1978–1981)
55 W P Thurston, Earthquakes in two-dimensional hyperbolic geometry, from: "Low-dimensional topology and Kleinian groups" (editor D B A Epstein), London Math. Soc. Lecture Note Ser. 112, Cambridge Univ. Press (1986) 91 MR903860
56 M Troyanov, Prescribing curvature on compact surfaces with conical singularities, Trans. Amer. Math. Soc. 324 (1991) 793 MR1005085
57 F Waldhausen, Eine Verallgemeinerung des Schleifensatzes, Topology 6 (1967) 501 MR0220300