Geometry & Topology Volume 26, issue 3 (2022)

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Counting hyperbolic multigeodesics with respect to the lengths of individual components and asymptotics of Weil–Petersson volumes

Francisco Arana-Herrera

Geometry & Topology 26 (2022) 1291–1347

DOI: 10.2140/gt.2022.26.1291

Bibliography

1	F Arana-Herrera, Counting square-tiled surfaces with prescribed real and imaginary foliations and connections to Mirzakhani’s asymptotics for simple closed hyperbolic geodesics, J. Mod. Dyn. 16 (2020) 81 MR4097720
2	F Arana-Herrera, Equidistribution of families of expanding horospheres on moduli spaces of hyperbolic surfaces, Geom. Dedicata 210 (2021) 65 MR4200910
3	F Arana-Herrera, J S Athreya, Square-integrability of the Mirzakhani function and statistics of simple closed geodesics on hyperbolic surfaces, Forum Math. Sigma 8 (2020) MR4061979
4	V Delecroix, É Goujard, P Zograf, A Zorich, Masur–Veech volumes, frequencies of simple closed geodesics, and intersection numbers of moduli spaces of curves, Duke Math. J. 170 (2021) 2633 MR4305379
5	N Do, Moduli spaces of hyperbolic surfaces and their Weil–Petersson volumes, from: "Handbook of moduli, I" (editors G Farkas, I Morrison), Adv. Lect. Math. 24, International (2013) 217 MR3184165
6	V Erlandsson, G Mondello, Ergodic invariant measures on the space of geodesic currents, preprint (2018) arXiv:1807.02144
7	V Erlandsson, H Parlier, J Souto, Counting curves, and the stable length of currents, J. Eur. Math. Soc. 22 (2020) 1675 MR4092896
8	V Erlandsson, J Souto, Counting curves in hyperbolic surfaces, Geom. Funct. Anal. 26 (2016) 729 MR3540452
9	V Erlandsson, J Souto, Mirzakhani’s curve counting and geodesic currents, book manuscript (2021)
10	V Erlandsson, C Uyanik, Length functions on currents and applications to dynamics and counting, from: "In the tradition of Thurston : geometry and topology" (editors K Ohshika, A Papadopoulos), Springer (2020) 423 MR4264584
11	A Eskin, M Mirzakhani, A Mohammadi, Effective counting of simple closed geodesics on hyperbolic surfaces, J. Eur. Math. Soc. (2021)
12	B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
13	A Fathi, F Laudenbach, V Poénaru, Thurston’s work on surfaces, 48, Princeton Univ. Press (2012) MR3053012
14	S P Kerckhoff, The Nielsen realization problem, Ann. of Math. 117 (1983) 235 MR690845
15	D Y Kleinbock, G A Margulis, Bounded orbits of nonquasiunipotent flows on homogeneous spaces, from: "Sinai’s Moscow Seminar on Dynamical Systems" (editors L A Bunimovich, B M Gurevich, Y B Pesin), Amer. Math. Soc. Transl. 171, Amer. Math. Soc. (1996) 141 MR1359098
16	M Liu, Length statistics of random multicurves on closed hyperbolic surfaces, preprint (2019) arXiv:1912.11155
17	G A Margulis, On some aspects of the theory of Anosov systems, PhD thesis, Moscow State University (1970) MR2035655
18	B Martelli, An introduction to geometric topology, CreateSpace (2016)
19	H Masur, Ergodic actions of the mapping class group, Proc. Amer. Math. Soc. 94 (1985) 455 MR787893
20	M Mirzakhani, Simple geodesics on hyperbolic surfaces and the volume of the moduli space of curves, PhD thesis, Harvard University (2004) MR2705986
21	M Mirzakhani, Random hyperbolic surfaces and measured laminations, from: "In the tradition of Ahlfors–Bers, IV" (editors D Canary, J Gilman, J Heinonen, H Masur), Contemp. Math. 432, Amer. Math. Soc. (2007) 179 MR2342816
22	M Mirzakhani, Simple geodesics and Weil–Petersson volumes of moduli spaces of bordered Riemann surfaces, Invent. Math. 167 (2007) 179 MR2264808
23	M Mirzakhani, Weil–Petersson volumes and intersection theory on the moduli space of curves, J. Amer. Math. Soc. 20 (2007) 1 MR2257394
24	M Mirzakhani, Ergodic theory of the earthquake flow, Int. Math. Res. Not. 2008 (2008) MR2416997
25	M Mirzakhani, Growth of the number of simple closed geodesics on hyperbolic surfaces, Ann. of Math. 168 (2008) 97 MR2415399
26	M Mirzakhani, Counting mapping class group orbits on hyperbolic surfaces, preprint (2016) arXiv:1601.03342
27	L Monin, V Telpukhovskiy, On normalizations of Thurston measure on the space of measured laminations, Topology Appl. 267 (2019) MR4008568
28	A Papadopoulos, Sur le bord de Thurston de l’espace de Teichmüller d’une surface non compacte, Math. Ann. 282 (1988) 353 MR967017
29	A Papadopoulos, On Thurston’s boundary of Teichmüller space and the extension of earthquakes, Topology Appl. 41 (1991) 147 MR1135095
30	A Papadopoulos, R C Penner, The Weil–Petersson symplectic structure at Thurston’s boundary, Trans. Amer. Math. Soc. 335 (1993) 891 MR1089420
31	A Papadopoulos, W Su, On the Finsler structure of Teichmüller’s metric and Thurston’s metric, Expo. Math. 33 (2015) 30 MR3310926
32	R C Penner, J L Harer, Combinatorics of train tracks, 125, Princeton Univ. Press (1992) MR1144770
33	K Rafi, J Souto, Geodesic currents and counting problems, Geom. Funct. Anal. 29 (2019) 871 MR3962881
34	Y Sözen, F Bonahon, The Weil–Petersson and Thurston symplectic forms, Duke Math. J. 108 (2001) 581 MR1838662
35	W P Thurston, Minimal stretch maps between hyperbolic surfaces, preprint (1986) arXiv:math/9801039
36	S Wolpert, On the Weil–Petersson geometry of the moduli space of curves, Amer. J. Math. 107 (1985) 969 MR796909