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The shape of the filling-systole subspace in surface moduli space and critical points of the systole function

Yue Gao

Algebraic & Geometric Topology 24 (2024) 2011–2038
Bibliography
1 L V Ahlfors, Lectures on quasiconformal mappings, 10, Van Nostrand (1966) MR200442
2 H Akrout, Singularités topologiques des systoles généralisées, Topology 42 (2003) 291 MR1941437
3 J W Anderson, H Parlier, A Pettet, Small filling sets of curves on a surface, Topology Appl. 158 (2011) 84 MR2734699
4 J W Anderson, H Parlier, A Pettet, Relative shapes of thick subsets of moduli space, Amer. J. Math. 138 (2016) 473 MR3483473
5 P Buser, Geometry and spectra of compact Riemann surfaces, 106, Birkhäuser (1992) MR1183224
6 A Fletcher, J Kahn, V Markovic, The moduli space of Riemann surfaces of large genus, Geom. Funct. Anal. 23 (2013) 867 MR3061775
7 M Fortier Bourque, Hyperbolic surfaces with sublinearly many systoles that fill, Comment. Math. Helv. 95 (2020) 515 MR4152623
8 M Fortier Bourque, K Rafi, Local maxima of the systole function, J. Eur. Math. Soc. 24 (2022) 623 MR4382480
9 Y Gao, J Wang, The maximal systole of hyperbolic surfaces with maximal S3–extendable abelian symmetry, Pacific J. Math. 325 (2023) 85 MR4635387
10 J Harer, D Zagier, The Euler characteristic of the moduli space of curves, Invent. Math. 85 (1986) 457 MR0848681
11 L Ji, Well-rounded equivariant deformation retracts of Teichmüller spaces, Enseign. Math. 60 (2014) 109 MR3262437
12 Y Liu, Virtual homological eigenvalues and the Weil–Petersson translation length, Sci. China Math. 66 (2023) 2119 MR4629935
13 B Maskit, Comparison of hyperbolic and extremal lengths, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985) 381 MR0802500
14 H Masur, Geometry of Teichmüller space with the Teichmüller metric, from: "Geometry of Riemann surfaces and their moduli spaces" (editors L Ji, S A Wolpert, S T Yau), Surv. Differ. Geom. 14, International (2009) 295 MR2655331
15 M Mirzakhani, Simple geodesics and Weil–Petersson volumes of moduli spaces of bordered Riemann surfaces, Invent. Math. 167 (2007) 179 MR2264808
16 M Mirzakhani, Growth of Weil–Petersson volumes and random hyperbolic surfaces of large genus, J. Differential Geom. 94 (2013) 267 MR3080483
17 X Nie, Y Wu, Y Xue, Large genus asymptotics for lengths of separating closed geodesics on random surfaces, J. Topol. 16 (2023) 106 MR4532491
18 K Rafi, J Tao, The diameter of the thick part of moduli space and simultaneous Whitehead moves, Duke Math. J. 162 (2013) 1833 MR3079261
19 M Rupflin, P M Topping, Horizontal curves of hyperbolic metrics, Calc. Var. Partial Differential Equations 57 (2018) 106 MR3814649
20 P Schmutz Schaller, Systoles and topological Morse functions for Riemann surfaces, J. Differential Geom. 52 (1999) 407 MR1761080
21 K Strebel, Quadratic differentials, 5, Springer (1984) MR743423
22 W P Thurston, Minimal stretch maps between hyperbolic surfaces, preprint (1986) arXiv:math/9801039 MR4554454
23 W P Thurston, A spine for Teichmüller space, preprint (1986)
24 S A Wolpert, Geodesic length functions and the Nielsen problem, J. Differential Geom. 25 (1987) 275 MR0880186
25 Y Wu, Growth of the Weil–Petersson inradius of moduli space, Ann. Inst. Fourier (Grenoble) 69 (2019) 1309 MR3986917
26 Y Wu, A new uniform lower bound on Weil–Petersson distance, Calc. Var. Partial Differential Equations 61 (2022) 146 MR4433089