Volume 21, issue 1 (2021)

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The dual Bonahon–Schläfli formula

Filippo Mazzoli

Algebraic & Geometric Topology 21 (2021) 279–315
Bibliography
1 F Bonahon, The geometry of Teichmüller space via geodesic currents, Invent. Math. 92 (1988) 139 MR931208
2 F Bonahon, Shearing hyperbolic surfaces, bending pleated surfaces and Thurston’s symplectic form, Ann. Fac. Sci. Toulouse Math. 5 (1996) 233 MR1413855
3 F Bonahon, Geodesic laminations with transverse Hölder distributions, Ann. Sci. École Norm. Sup. 30 (1997) 205 MR1432054
4 F Bonahon, Transverse Hölder distributions for geodesic laminations, Topology 36 (1997) 103 MR1410466
5 F Bonahon, A Schläfli-type formula for convex cores of hyperbolic 3–manifolds, J. Differential Geom. 50 (1998) 25 MR1678473
6 F Bonahon, Variations of the boundary geometry of 3–dimensional hyperbolic convex cores, J. Differential Geom. 50 (1998) 1 MR1678469
7 M Bridgeman, J Brock, K Bromberg, Schwarzian derivatives, projective structures, and the Weil–Petersson gradient flow for renormalized volume, Duke Math. J. 168 (2019) 867 MR3934591
8 R D Canary, D Epstein, A Marden, editors, Fundamentals of hyperbolic geometry: selected expositions, 328, Cambridge Univ. Press (2006) MR2230672
9 C L Epstein, Envelopes of horospheres and Weingarten surfaces in hyperbolic 3–space, preprint (1984)
10 C D Hodgson, I Rivin, A characterization of compact convex polyhedra in hyperbolic 3–space, Invent. Math. 111 (1993) 77 MR1193599
11 L Keen, C Series, Continuity of convex hull boundaries, Pacific J. Math. 168 (1995) 183 MR1331998
12 S P Kerckhoff, Earthquakes are analytic, Comment. Math. Helv. 60 (1985) 17 MR787659
13 K Krasnov, J M Schlenker, On the renormalized volume of hyperbolic 3–manifolds, Comm. Math. Phys. 279 (2008) 637 MR2386723
14 K Krasnov, J M Schlenker, A symplectic map between hyperbolic and complex Teichmüller theory, Duke Math. J. 150 (2009) 331 MR2569616
15 F Mazzoli, The dual volume of quasifuchsian manifolds and the Weil–Petersson distance, preprint (2019) arXiv:1907.04754
16 F Mazzoli, Constant curvature surfaces and volumes of convex co-compact hyperbolic manifolds, PhD thesis, Université du Luxembourg (2020)
17 I Rivin, J M Schlenker, The Schläfli formula in Einstein manifolds with boundary, Electron. Res. Announc. Amer. Math. Soc. 5 (1999) 18 MR1669399
18 H L Royden, Real analysis, Macmillan (1963) MR0151555
19 L Schläfli, On the multiple integral ndx dydz, whose limits are p1 = a1x + b1y + + h1z > 0, p2 > 0,,pn > 0, and x2 + y2 + + z2 < 1, Q. J. Pure Appl. Math. 168 (1858) 269
20 J M Schlenker, The renormalized volume and the volume of the convex core of quasifuchsian manifolds, Math. Res. Lett. 20 (2013) 773 MR3188032
21 J M Schlenker, Notes on the Schwarzian tensor and measured foliations at infinity of quasifuchsian manifolds, preprint (2017) arXiv:1708.01852
22 D Sullivan, Travaux de Thurston sur les groupes quasi-fuchsiens et les variétés hyperboliques de dimension 3 fibrées sur S1, from: "Séminaire Bourbaki, 1979/1980", Lecture Notes in Math. 842, Springer (1981) 196 MR636524
23 W P Thurston, The geometry and topology of three-manifolds, lecture notes (1980)