Algebraic & Geometric Topology Volume 23, issue 8 (2023)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Pressure metrics for deformation spaces of quasifuchsian groups with parabolics

Harrison Bray, Richard Canary and Lien-Yung Kao

Algebraic & Geometric Topology 23 (2023) 3615–3653

DOI: 10.2140/agt.2023.23.3615

Bibliography

1	K Astala, T Iwaniec, G Martin, Elliptic partial differential equations and quasiconformal mappings in the plane, 48, Princeton Univ. Press (2009) MR2472875
2	L Bers, Simultaneous uniformization, Bull. Amer. Math. Soc. 66 (1960) 94 MR111834
3	C Bishop, T Steger, Representation-theoretic rigidity in PSL(2, ℝ), Acta Math. 170 (1993) 121 MR1208564
4	F Bonahon, The geometry of Teichmüller space via geodesic currents, Invent. Math. 92 (1988) 139 MR931208
5	F Bonahon, Kleinian groups which are almost Fuchsian, J. Reine Angew. Math. 587 (2005) 1 MR2186972
6	R Bowen, Hausdorff dimension of quasicircles, Inst. Hautes Études Sci. Publ. Math. 50 (1979) 11 MR556580
7	R Bowen, C Series, Markov maps associated with Fuchsian groups, Inst. Hautes Études Sci. Publ. Math. 50 (1979) 153 MR556585
8	H Bray, R Canary, L Y Kao, G Martone, Counting, equidistribution and entropy gaps at infinity with applications to cusped Hitchin representations, J. Reine Angew. Math. 791 (2022) 1 MR4489624
9	M Bridgeman, Hausdorff dimension and the Weil–Petersson extension to quasifuchsian space, Geom. Topol. 14 (2010) 799 MR2602852
10	M Bridgeman, R Canary, F Labourie, A Sambarino, The pressure metric for Anosov representations, Geom. Funct. Anal. 25 (2015) 1089 MR3385630
11	M Bridgeman, R Canary, A Sambarino, An introduction to pressure metrics for higher Teichmüller spaces, Ergodic Theory Dynam. Systems 38 (2018) 2001 MR3833339
12	M Burger, Intersection, the Manhattan curve, and Patterson–Sullivan theory in rank 2, Int. Math. Res. Not. (1993) 217 MR1230298
13	R D Canary, M Culler, S Hersonsky, P B Shalen, Approximation by maximal cusps in boundaries of deformation spaces of Kleinian groups, J. Differential Geom. 64 (2003) 57 MR2015044
14	F Dal’bo, J P Otal, M Peigné, Séries de Poincaré des groupes géométriquement finis, Israel J. Math. 118 (2000) 109 MR1776078
15	F Dal’bo, M Peigné, Groupes du ping-pong et géodésiques fermées en courbure −1, Ann. Inst. Fourier (Grenoble) 46 (1996) 755 MR1411728
16	F Dal’bo, M Peigné, Some negatively curved manifolds with cusps, mixing and counting, J. Reine Angew. Math. 497 (1998) 141 MR1617430
17	A Douady, C J Earle, Conformally natural extension of homeomorphisms of the circle, Acta Math. 157 (1986) 23 MR857678
18	A Fathi, L Flaminio, Infinitesimal conjugacies and Weil–Petersson metric, Ann. Inst. Fourier (Grenoble) 43 (1993) 279 MR1209705
19	G Iommi, T Jordan, Phase transitions for suspension flows, Comm. Math. Phys. 320 (2013) 475 MR3053770
20	G Iommi, F Riquelme, A Velozo, Entropy in the cusp and phase transitions for geodesic flows, Israel J. Math. 225 (2018) 609 MR3805660
21	L Y Kao, Pressure type metrics on spaces of metric graphs, Geom. Dedicata 187 (2017) 151 MR3622688
22	L Y Kao, Manhattan curves for hyperbolic surfaces with cusps, Ergodic Theory Dynam. Systems 40 (2020) 1843 MR4108907
23	L Y Kao, Pressure metrics and Manhattan curves for Teichmüller spaces of punctured surfaces, Israel J. Math. 240 (2020) 567 MR4193143
24	M Kapovich, Hyperbolic manifolds and discrete groups, 183, Birkhäuser (2001) MR1792613
25	I Kim, Marked length rigidity of rank one symmetric spaces and their product, Topology 40 (2001) 1295 MR1867246
26	G Knieper, Volume growth, entropy and the geodesic stretch, Math. Res. Lett. 2 (1995) 39 MR1312976
27	F Ledrappier, O Sarig, Fluctuations of ergodic sums for horocycle flows on ℤ^d–covers of finite volume surfaces, Discrete Contin. Dyn. Syst. 22 (2008) 247 MR2410958
28	B Maskit, On boundaries of Teichmüller spaces and on Kleinian groups, II, Ann. of Math. 91 (1970) 607 MR297993
29	R D Mauldin, M Urbański, Graph directed Markov systems : geometry and dynamics of limit sets, 148, Cambridge Univ. Press (2003) MR2003772
30	C T McMullen, Thermodynamics, dimension and the Weil–Petersson metric, Invent. Math. 173 (2008) 365 MR2415311
31	S J Patterson, The limit set of a Fuchsian group, Acta Math. 136 (1976) 241 MR450547
32	F Paulin, M Pollicott, B Schapira, Equilibrium states in negative curvature, 373, Soc. Math. France (2015) MR3444431
33	M Pollicott, R Sharp, A Weil–Petersson type metric on spaces of metric graphs, Geom. Dedicata 172 (2014) 229 MR3253781
34	F Riquelme, A Velozo, Escape of mass and entropy for geodesic flows, Ergodic Theory Dynam. Systems 39 (2019) 446 MR3893267
35	T Roblin, Ergodicité et équidistribution en courbure négative, 95, Soc. Math. France (2003) MR2057305
36	D Ruelle, Repellers for real analytic maps, Ergodic Theory Dynam. Systems 2 (1982) 99 MR684247
37	O M Sarig, Thermodynamic formalism for countable Markov shifts, Ergodic Theory Dynam. Systems 19 (1999) 1565 MR1738951
38	O Sarig, Existence of Gibbs measures for countable Markov shifts, Proc. Amer. Math. Soc. 131 (2003) 1751 MR1955261
39	O Sarig, Thermodynamic formalism for topological Markov shifts, lecture notes (2009)
40	B Schapira, S Tapie, Regularity of entropy, geodesic currents and entropy at infinity, Ann. Sci. Éc. Norm. Supér. 54 (2021) 1 MR4245867
41	R Sharp, The Manhattan curve and the correlation of length spectra on hyperbolic surfaces, Math. Z. 228 (1998) 745 MR1644452
42	M Stadlbauer, The return sequence of the Bowen–Series map for punctured surfaces, Fund. Math. 182 (2004) 221 MR2098779
43	D Sullivan, The density at infinity of a discrete group of hyperbolic motions, Inst. Hautes Études Sci. Publ. Math. 50 (1979) 171 MR556586
44	D Sullivan, Discrete conformal groups and measurable dynamics, Bull. Amer. Math. Soc. 6 (1982) 57 MR634434
45	D Sullivan, Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math. 153 (1984) 259 MR766265
46	D Sullivan, Quasiconformal homeomorphisms and dynamics, II : Structural stability implies hyperbolicity for Kleinian groups, Acta Math. 155 (1985) 243 MR806415
47	D Sullivan, Related aspects of positivity in Riemannian geometry, J. Differential Geom. 25 (1987) 327 MR882827
48	S A Wolpert, Thurston’s Riemannian metric for Teichmüller space, J. Differential Geom. 23 (1986) 143 MR845703
49	X Xie, A Bowen type rigidity theorem for non-cocompact hyperbolic groups, Math. Z. 259 (2008) 249 MR2390079