Geometry & Topology Volume 23, issue 1 (2019)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Rigidity of convex divisible domains in flag manifolds

Wouter Van Limbeek and Andrew Zimmer

Geometry & Topology 23 (2019) 171–240

DOI: 10.2140/gt.2019.23.171

Bibliography

1	R C Alperin, An elementary account of Selberg’s lemma, Enseign. Math. 33 (1987) 269 MR925989
2	S A Ballas, J Danciger, G S Lee, Convex projective structures on nonhyperbolic three-manifolds, Geom. Topol. 22 (2018) 1593 MR3780442
3	W Ballmann, Nonpositively curved manifolds of higher rank, Ann. of Math. 122 (1985) 597 MR819559
4	T J Barth, Convex domains and Kobayashi hyperbolicity, Proc. Amer. Math. Soc. 79 (1980) 556 MR572300
5	Y Benoist, Automorphismes des cônes convexes, Invent. Math. 141 (2000) 149 MR1767272
6	Y Benoist, Convexes divisibles, II, Duke Math. J. 120 (2003) 97 MR2010735
7	Y Benoist, Convexes hyperboliques et fonctions quasisymétriques, Publ. Math. Inst. Hautes Études Sci. 97 (2003) 181 MR2010741
8	Y Benoist, Convexes divisibles, I, from: "Algebraic groups and arithmetic" (editors S G Dani, G Prasad), Tata Inst. Fund. Res. (2004) 339 MR2094116
9	Y Benoist, Convexes divisibles, IV : Structure du bord en dimension 3, Invent. Math. 164 (2006) 249 MR2218481
10	Y Benoist, A survey on divisible convex sets, from: "Geometry, analysis and topology of discrete groups" (editors L Ji, K Liu, L Yang, S T Yau), Adv. Lect. Math. 6, Int. (2008) 1 MR2464391
11	J P Benzécri, Sur les variétés localement affines et localement projectives, Bull. Soc. Math. France 88 (1960) 229 MR0124005
12	A Borel, Linear algebraic groups, 126, Springer (1991) MR1102012
13	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
14	K S Brown, Cohomology of groups, 87, Springer (1994) MR1324339
15	K Burns, R Spatzier, Manifolds of nonpositive curvature and their buildings, Inst. Hautes Études Sci. Publ. Math. 65 (1987) 35 MR908215
16	K Burns, R Spatzier, On topological Tits buildings and their classification, Inst. Hautes Études Sci. Publ. Math. 65 (1987) 5 MR908214
17	S Choi, G S Lee, L Marquis, Convex projective generalized Dehn filling, preprint (2016) arXiv:1611.02505
18	S Choi, G S Lee, L Marquis, Deformations of convex real projective manifolds and orbifolds, preprint (2016) arXiv:1605.02548
19	D Cooper, D D Long, S Tillmann, On convex projective manifolds and cusps, Adv. Math. 277 (2015) 181 MR3336086
20	M Crampon, Entropies of strictly convex projective manifolds, J. Mod. Dyn. 3 (2009) 511 MR2587084
21	B Farb, S Weinberger, Isometries, rigidity and universal covers, Ann. of Math. 168 (2008) 915 MR2456886
22	S Frankel, Complex geometry of convex domains that cover varieties, Acta Math. 163 (1989) 109 MR1007621
23	S Frankel, Applications of affine geometry to geometric function theory in several complex variables, I : Convergent rescalings and intrinsic quasi-isometric structure, from: "Several complex variables and complex geometry, II" (editors E Bedford, J P D’Angelo, R E Greene, S G Krantz), Proc. Sympos. Pure Math. 52, Amer. Math. Soc. (1991) 183 MR1128543
24	W Fulton, J Harris, Representation theory: a first course, 129, Springer (1991) MR1153249
25	A Geng, When are radicals of Lie groups lattice-hereditary ?, New York J. Math. 21 (2015) 321 MR3358545
26	W M Goldman, Convex real projective structures on compact surfaces, J. Differential Geom. 31 (1990) 791 MR1053346
27	F Guéritaud, O Guichard, F Kassel, A Wienhard, Compactification of certain Clifford–Klein forms of reductive homogeneous spaces, Michigan Math. J. 66 (2017) 49 MR3619735
28	O Guichard, A Wienhard, Convex foliated projective structures and the Hitchin component for PSL₄(ℝ), Duke Math. J. 144 (2008) 381 MR2444302
29	O Guichard, A Wienhard, Anosov representations: domains of discontinuity and applications, Invent. Math. 190 (2012) 357 MR2981818
30	S Helgason, Differential geometry, Lie groups, and symmetric spaces, 80, Academic (1978) MR514561
31	D Johnson, J J Millson, Deformation spaces associated to compact hyperbolic manifolds, from: "Discrete groups in geometry and analysis" (editor R Howe), Progr. Math. 67, Birkhäuser (1987) 48 MR900823
32	M Kapovich, Convex projective structures on Gromov–Thurston manifolds, Geom. Topol. 11 (2007) 1777 MR2350468
33	M Kapovich, B Leeb, J Porti, Dynamics on flag manifolds: domains of proper discontinuity and cocompactness, Geom. Topol. 22 (2018) 157 MR3720343
34	A Karlsson, G A Noskov, The Hilbert metric and Gromov hyperbolicity, Enseign. Math. 48 (2002) 73 MR1923418
35	K T Kim, On the automorphism groups of convex domains in ℂⁿ, Adv. Geom. 4 (2004) 33 MR2155363
36	K T Kim, S G Krantz, Complex scaling and geometric analysis of several variables, Bull. Korean Math. Soc. 45 (2008) 523 MR2442193
37	S Kobayashi, Intrinsic distances associated with flat affine or projective structures, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24 (1977) 129 MR0445016
38	J L Koszul, Déformations de connexions localement plates, Ann. Inst. Fourier (Grenoble) 18 (1968) 103 MR0239529
39	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
40	T Nagano, Transformation groups on compact symmetric spaces, Trans. Amer. Math. Soc. 118 (1965) 428 MR0182937
41	A Onishchik, È Vinberg, Lie groups and Lie algebras, III: Structure of Lie groups and Lie algebras, 41, Springer (1994)
42	G Prasad, ℝ–regular elements in Zariski-dense subgroups, Quart. J. Math. Oxford Ser. 45 (1994) 541 MR1315463
43	J F Quint, Convexes divisibles (d’après Yves Benoist), from: "Séminaire Bourbaki", Astérisque 332, Soc. Mat. de France (2010) 45 MR2648674
44	M S Raghunathan, Discrete subgroups of Lie groups, 68, Springer (1972) MR0507234
45	J Vey, Sur les automorphismes affines des ouverts convexes saillants, Ann. Scuola Norm. Sup. Pisa 24 (1970) 641 MR0283720
46	È B Vinberg, Discrete linear groups that are generated by reflections, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971) 1072 MR0302779
47	È B Vinberg, V G Kac, Quasi-homogeneous cones, Mat. Zametki 1 (1967) 347 MR0208470
48	A Zimmer, Proper quasi-homogeneous domains in flag manifolds and geometric structures, preprint (2015) arXiv:1507.06921