Geometry & Topology Volume 27, issue 9 (2023)

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Moduli of spherical tori with one conical point

Alexandre Eremenko, Gabriele Mondello and Dmitri Panov

Geometry & Topology 27 (2023) 3619–3698

DOI: 10.2140/gt.2023.27.3619

Bibliography

1	D Burago, Y Burago, S Ivanov, A course in metric geometry, 33, Amer. Math. Soc. (2001) MR1835418
2	C L Chai, C S Lin, C L Wang, Mean field equations, hyperelliptic curves and modular forms, I, Camb. J. Math. 3 (2015) 127 MR3356357
3	C C Chen, C S Lin, Mean field equation of Liouville type with singular data : topological degree, Comm. Pure Appl. Math. 68 (2015) 887 MR3340376
4	Q Chen, W Wang, Y Wu, B Xu, Conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces, Pacific J. Math. 273 (2015) 75 MR3290445
5	Z Chen, T J Kuo, C S Lin, Existence and non-existence of solutions of the mean field equations on flat tori, Proc. Amer. Math. Soc. 145 (2017) 3989 MR3665050
6	Z Chen, C S Lin, Critical points of the classical Eisenstein series of weight two, J. Differential Geom. 113 (2019) 189 MR4023291
7	D Cooper, C D Hodgson, S P Kerckhoff, Three-dimensional orbifolds and cone-manifolds, 5, Math. Soc. Japan (2000) MR1778789
8	B Delaunay, Sur la sphère vide, Bull. Acad. Sci. URSS (1934) 793
9	A Eremenko, Metrics of positive curvature with conic singularities on the sphere, Proc. Amer. Math. Soc. 132 (2004) 3349 MR2073312
10	A Eremenko, Metrics of constant positive curvature with four conic singularities on the sphere, Proc. Amer. Math. Soc. 148 (2020) 3957 MR4127839
11	A Eremenko, A Gabrielov, On metrics of curvature 1 with four conic singularities on tori and on the sphere, Illinois J. Math. 59 (2015) 925 MR3628295
12	A Eremenko, A Gabrielov, The space of Schwarz–Klein spherical triangles, J. Math. Phys. Anal. Geom. 16 (2020) 263 MR4252709
13	A Eremenko, A Gabrielov, G Mondello, D Panov, Moduli spaces for Lamé functions and abelian differentials of the second kind, Commun. Contemp. Math. 24 (2022) 2150028 MR4380114
14	A Eremenko, V Tarasov, Fuchsian equations with three non-apparent singularities, Symmetry Integrability Geom. Methods Appl. 14 (2018) 058 MR3814567
15	M Gromov, Metric structures for Riemannian and non-Riemannian spaces, Birkhäuser (2007) MR2307192
16	J Harer, D Zagier, The Euler characteristic of the moduli space of curves, Invent. Math. 85 (1986) 457 MR848681
17	F Klein, Vorlesungen über die hypergeometrische Funktion, 39, Springer (1933) 344
18	L Li, J Song, B Xu, Irreducible cone spherical metrics and stable extensions of two line bundles, Adv. Math. 388 (2021) 107854 MR4283757
19	C S Lin, C L Wang, Elliptic functions, Green functions and the mean field equations on tori, Ann. of Math. 172 (2010) 911 MR2680484
20	C S Lin, C L Wang, Mean field equations, hyperelliptic curves and modular forms, II, J. Éc. polytech. Math. 4 (2017) 557 MR3665608
21	R S Maier, Lamé polynomials, hyperelliptic reductions and Lamé band structure, Philos. Trans. Roy. Soc. Lond. Ser. A 366 (2008) 1115 MR2377687
22	G Mondello, D Panov, Spherical metrics with conical singularities on a 2–sphere : angle constraints, Int. Math. Res. Not. 2016 (2016) 4937 MR3556430
23	G Mondello, D Panov, Spherical surfaces with conical points: systole inequality and moduli spaces with many connected components, Geom. Funct. Anal. 29 (2019) 1110 MR3990195
24	I Pak, Lectures on discrete and polyhedral geometry, (2010)
25	H P de Saint-Gervais, Uniformization of Riemann surfaces, Eur. Math. Soc. (2016) MR3494804
26	J Song, Y Cheng, B Li, B Xu, Drawing cone spherical metrics via Strebel differentials, Int. Math. Res. Not. 2020 (2020) 3341 MR4123106
27	G Tarantello, Analytical, geometrical and topological aspects of a class of mean field equations on surfaces, Discrete Contin. Dyn. Syst. 28 (2010) 931 MR2644774
28	W P Thurston, Shapes of polyhedra and triangulations of the sphere, from: "The Epstein birthday schrift" (editors I Rivin, C Rourke, C Series), Geom. Topol. Monogr. 1, Geom. Topol. Publ. (1998) 511 MR1668340
29	E T Whittaker, G N Watson, A course of modern analysis, Cambridge Univ. Press (1996) MR1424469