Volume 17, issue 1 (2013)

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Cubic differentials and finite volume convex projective surfaces

Yves Benoist and Dominique Hulin

Geometry & Topology 17 (2013) 595–620
Bibliography
1 L V Ahlfors, An extension of Schwarz’s lemma, Trans. Amer. Math. Soc. 43 (1938) 359 MR1501949
2 J P Benzécri, Sur les variétés localement affines et localement projectives, Bull. Soc. Math. France 88 (1960) 229 MR0124005
3 E Calabi, Complete affine hyperspheres, I, from: "Symposia Mathematica, Vol. X", Academic Press (1972) 19 MR0365607
4 S Y Cheng, S T Yau, On the regularity of the Monge–Ampère equation det(2u∕∂xi∂xj) = F(x,u), Comm. Pure Appl. Math. 30 (1977) 41 MR0437805
5 S Y Cheng, S T Yau, Complete affine hypersurfaces, I, The completeness of affine metrics, Comm. Pure Appl. Math. 39 (1986) 839 MR859275
6 S Gigena, On a conjecture by E. Calabi, Geom. Dedicata 11 (1981) 387 MR637915
7 D Gilbarg, N S Trudinger, Elliptic partial differential equations of second order, , Springer (2001) MR1814364
8 W Goldman, Projective geometry on manifolds, Lecture notes (1988)
9 W M Goldman, Convex real projective structures on compact surfaces, J. Differential Geom. 31 (1990) 791 MR1053346
10 F Labourie, Flat projective structures on surfaces and cubic holomorphic differentials, Pure Appl. Math. Q. 3 (2007) 1057 MR2402597
11 J Lee, Convex fundamental domains for properly convex real projective structures
12 A M Li, Calabi conjecture on hyperbolic affine hyperspheres, II, Math. Ann. 293 (1992) 485 MR1170522
13 J Loftin, Applications of affine differential geometry to P2 surfaces, PhD thesis, Rutgers University (1999)
14 J C Loftin, Affine spheres and convex Pn–manifolds, Amer. J. Math. 123 (2001) 255 MR1828223
15 J C Loftin, The compactification of the moduli space of convex P2 surfaces, I, J. Differential Geom. 68 (2004) 223 MR2144248
16 J Loftin, Survey on affine spheres, from: "Handbook of geometric analysis, No. 2" (editors L Ji, P Li, R Schoen, L Simon), Adv. Lect. Math. (ALM) 13, Int. Press, Somerville, MA (2010) 161 MR2743442
17 L Marquis, Espace des modules marqués des surfaces projectives convexes de volume fini, Geom. Topol. 14 (2010) 2103 MR2740643
18 L Marquis, Surface projective convexe de volume fini, Ann. Inst. Fourier (Grenoble) 62 (2012) 325 MR2986273
19 K Nomizu, T Sasaki, Affine differential geometry, 111, Cambridge Univ. Press (1994) MR1311248
20 M Troyanov, The Schwarz lemma for nonpositively curved Riemannian surfaces, Manuscripta Math. 72 (1991) 251 MR1118545
21 N S Trudinger, X J Wang, The Monge–Ampère equation and its geometric applications, from: "Handbook of geometric analysis, No. 1" (editors L Ji, P Li, R Schoen, L Simon), Adv. Lect. Math. (ALM) 7, Int. Press, Somerville, MA (2008) 467 MR2483373
22 C P Wang, Some examples of complete hyperbolic affine 2–spheres in 3, from: "Global differential geometry and global analysis" (editors D Ferus, U Pinkall, U Simon, B Wegner), Lecture Notes in Math. 1481, Springer (1991) 271 MR1178538
23 S T Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975) 201 MR0431040