Volume 22, issue 3 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Deforming convex projective manifolds

Daryl Cooper, Darren Long and Stephan Tillmann

Geometry & Topology 22 (2018) 1349–1404
Bibliography
1 M Baker, D Cooper, A combination theorem for convex hyperbolic manifolds, with applications to surfaces in 3–manifolds, J. Topol. 1 (2008) 603 MR2417445
2 S A Ballas, Finite volume properly convex deformations of the figure-eight knot, Geom. Dedicata 178 (2015) 49 MR3397481
3 S Ballas, D Cooper, A Leitner, Generalized cusps in real projective manifolds: classification, preprint (2017) arXiv:1710.03132
4 Y Benoist, Convexes divisibles, IV : Structure du bord en dimension 3, Invent. Math. 164 (2006) 249 MR2218481
5 J P Benzécri, Sur les variétés localement affines et localement projectives, Bull. Soc. Math. France 88 (1960) 229 MR0124005
6 R D Canary, D B A Epstein, P Green, Notes on notes of Thurston, from: "Analytical and geometric aspects of hyperbolic space" (editor D B A Epstein), London Math. Soc. Lecture Note Ser. 111, Cambridge Univ. Press (1987) 3 MR903850
7 S Choi, Geometric structures on orbifolds and holonomy representations, Geom. Dedicata 104 (2004) 161 MR2043960
8 S Choi, The convex real projective orbifolds with radial or totally geodesic ends: the closedness and openness of deformations, preprint (2010) arXiv:1011.1060
9 S Choi, The classification of ends of properly convex real projective orbifolds, II: Properly convex radial ends and totally geodesic ends, preprint (2015) arXiv:1501.00352
10 B Chow, S C Chu, D Glickenstein, C Guenther, J Isenberg, T Ivey, D Knopf, P Lu, F Luo, L Ni, The Ricci flow : techniques and applications, III : Geometric-analytic aspects, 163, Amer. Math. Soc. (2010) MR2604955
11 D Cooper, J Danciger, A Wienhard, Limits of geometries, preprint (2014) arXiv:1408.4109
12 D Cooper, D D Long, A generalization of the Epstein–Penner construction to projective manifolds, Proc. Amer. Math. Soc. 143 (2015) 4561 MR3373953
13 D Cooper, D D Long, S Tillmann, On convex projective manifolds and cusps, Adv. Math. 277 (2015) 181 MR3336086
14 M Crampon, L Marquis, Un lemme de Kazhdan–Margulis–Zassenhaus pour les géométries de Hilbert, Ann. Math. Blaise Pascal 20 (2013) 363 MR3138033
15 M Crampon, L Marquis, Finitude géométrique en géométrie de Hilbert, Ann. Inst. Fourier (Grenoble) 64 (2014) 2299 MR3331168
16 J Faraut, A Korányi, Analysis on symmetric cones, Clarendon (1994) MR1446489
17 W M Goldman, Geometric structures on manifolds and varieties of representations, from: "Geometry of group representations" (editors W M Goldman, A R Magid), Contemp. Math. 74, Amer. Math. Soc. (1988) 169 MR957518
18 W Goldman, Geometric structures on manifolds, book project (2016)
19 R E Greene, H Wu, Approximation theorems, C convex exhaustions and manifolds of positive curvature, Bull. Amer. Math. Soc. 81 (1975) 101 MR0362137
20 R E Greene, H Wu, C convex functions and manifolds of positive curvature, Acta Math. 137 (1976) 209 MR0458336
21 M W Hirsch, Differential topology, 33, Springer (1976) MR0448362
22 M W Hirsch, B Mazur, Smoothings of piecewise linear manifolds, 80, Princeton Univ. Press (1974) MR0415630
23 M Koecher, Positivitätsbereiche im Rn, Amer. J. Math. 79 (1957) 575 MR0090771
24 J L Koszul, Variétés localement plates et convexité, Osaka J. Math. 2 (1965) 285 MR0196662
25 J L Koszul, Déformations de connexions localement plates, Ann. Inst. Fourier (Grenoble) 18 (1968) 103 MR0239529
26 A Leitner, A classification of subgroups of SL(4, ) isomorphic to 3 and generalized cusps in projective 3 manifolds, Topology Appl. 206 (2016) 241 MR3494445
27 E L Lima, On the local triviality of the restriction map for embeddings, Comment. Math. Helv. 38 (1964) 163 MR0161343
28 L Marquis, Espace des modules marqués des surfaces projectives convexes de volume fini, Geom. Topol. 14 (2010) 2103 MR2740643
29 L Marquis, Surface projective convexe de volume fini, Ann. Inst. Fourier (Grenoble) 62 (2012) 325 MR2986273
30 L Marquis, Around groups in Hilbert geometry, from: "Handbook of Hilbert geometry" (editors A Papadopoulos, M Troyanov), IRMA Lect. Math. Theor. Phys. 22, Eur. Math. Soc. (2014) 207 MR3329882
31 A Papadopoulos, M Troyanov, Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry, Expo. Math. 27 (2009) 109 MR2518619
32 R Schoen, S T Yau, Lectures on differential geometry, 1, International (1994) MR1333601
33 H Shima, The geometry of Hessian structures, World Sci. (2007) MR2293045
34 H Shima, K Yagi, Geometry of Hessian manifolds, Differential Geom. Appl. 7 (1997) 277 MR1480540
35 P A N Smith, Counterexamples to smoothing convex functions, Canad. Math. Bull. 29 (1986) 308 MR846709
36 L F Tam, Exhaustion functions on complete manifolds, from: "Recent advances in geometric analysis" (editors Y I Lee, C S Lin, M P Tsui), Adv. Lect. Math. 11, International (2010) 211 MR2648946
37 W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
38 È B Vinberg, The theory of homogeneous convex cones, Trudy Moskov. Mat. Obšč. 12 (1963) 303 MR0158414
39 J H C Whitehead, On C1–complexes, Ann. of Math. 41 (1940) 809 MR0002545
40 D Witte, Superrigidity of lattices in solvable Lie groups, Invent. Math. 122 (1995) 147 MR1354957