Volume 22, issue 4 (2018)

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Normalized entropy versus volume for pseudo-Anosovs

Sadayoshi Kojima and Greg McShane

Geometry & Topology 22 (2018) 2403–2426
Bibliography
1 I Agol, Ideal triangulations of pseudo-Anosov mapping tori, from: "Topology and geometry in dimension three" (editors W Li, L Bartolini, J Johnson, F Luo, R Myers, J H Rubinstein), Contemp. Math. 560, Amer. Math. Soc. (2011) 1 MR2866919
2 L Bers, Simultaneous uniformization, Bull. Amer. Math. Soc. 66 (1960) 94 MR0111834
3 L Bers, An extremal problem for quasiconformal mappings and a theorem by Thurston, Acta Math. 141 (1978) 73 MR0477161
4 M Bridgeman, Average bending of convex pleated planes in hyperbolic three-space, Invent. Math. 132 (1998) 381 MR1621436
5 J F Brock, Weil–Petersson translation distance and volumes of mapping tori, Comm. Anal. Geom. 11 (2003) 987 MR2032506
6 J Brock, K Bromberg, Geometric inflexibility and 3–manifolds that fiber over the circle, J. Topol. 4 (2011) 1 MR2783376
7 C Cao, G R Meyerhoff, The orientable cusped hyperbolic 3–manifolds of minimum volume, Invent. Math. 146 (2001) 451 MR1869847
8 C Epstein, Envelopes of horospheres and Weingarten surfaces in hyperbolic 3–spaces, preprint (1984)
9 D B A Epstein, A Marden, V Markovic, Quasiconformal homeomorphisms and the convex hull boundary, Ann. of Math. 159 (2004) 305 MR2052356
10 B Farb, C J Leininger, D Margalit, Small dilatation pseudo-Anosov homeomorphisms and 3–manifolds, Adv. Math. 228 (2011) 1466 MR2824561
11 F P Gardiner, N Lakic, Quasiconformal Teichmüller theory, 76, Amer. Math. Soc. (2000) MR1730906
12 J H Hubbard, Teichmüller theory and applications to geometry, topology, and dynamics, I, Matrix Editions (2006) MR2245223
13 E Kin, S Kojima, M Takasawa, Entropy versus volume for pseudo-Anosovs, Experiment. Math. 18 (2009) 397 MR2583541
14 S Kojima, Entropy, Weil–Petersson translation distance and Gromov norm for surface automorphisms, Proc. Amer. Math. Soc. 140 (2012) 3993 MR2944738
15 K Krasnov, J M Schlenker, On the renormalized volume of hyperbolic 3–manifolds, Comm. Math. Phys. 279 (2008) 637 MR2386723
16 C T McMullen, Renormalization and 3–manifolds which fiber over the circle, 142, Princeton Univ. Press (1996) MR1401347
17 Y N Minsky, Bounded geometry for Kleinian groups, Invent. Math. 146 (2001) 143 MR1859020
18 Z Nehari, The Schwarzian derivative and schlicht functions, Bull. Amer. Math. Soc. 55 (1949) 545 MR0029999
19 R C Penner, Bounds on least dilatations, Proc. Amer. Math. Soc. 113 (1991) 443 MR1068128
20 K Rafi, A characterization of short curves of a Teichmüller geodesic, Geom. Topol. 9 (2005) 179 MR2115672
21 J M Schlenker, The renormalized volume and the volume of the convex core of quasifuchsian manifolds, Math. Res. Lett. 20 (2013) 773 MR3188032
22 J M Schlenker, The renormalized volume and the volume of the convex core of quasifuchsian manifolds, v4, revision (2017) arXiv:1109.6663v4
23 W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
24 W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417 MR956596
25 W P Thurston, Hyperbolic structures on 3–manifolds, II : Surface groups and 3–manifolds which fiber over the circle, preprint (1998) arXiv:math/9801045