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A higher-rank rigidity theorem for convex real projective manifolds

Andrew Zimmer

Geometry & Topology 27 (2023) 2899–2936
Bibliography
1 W Ballmann, Axial isometries of manifolds of nonpositive curvature, Math. Ann. 259 (1982) 131 MR656659
2 W Ballmann, Nonpositively curved manifolds of higher rank, Ann. of Math. 122 (1985) 597 MR819559
3 W Ballmann, Lectures on spaces of nonpositive curvature, 25, Birkhäuser (1995) MR1377265
4 W Ballmann, P Eberlein, Fundamental groups of manifolds of nonpositive curvature, J. Differential Geom. 25 (1987) 1 MR873453
5 Y Benoist, Convexes divisibles, II, Duke Math. J. 120 (2003) 97 MR2010735
6 Y Benoist, Convexes divisibles, IV : Structure du bord en dimension 3, Invent. Math. 164 (2006) 249 MR2218481
7 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, International (2008) 1 MR2464391
8 Y Benoist, J F Quint, Random walks on reductive groups, 62, Springer (2016) MR3560700
9 J P Benzécri, Sur les variétés localement affines et localement projectives, Bull. Soc. Math. France 88 (1960) 229 MR124005
10 A Borel, Compact Clifford–Klein forms of symmetric spaces, Topology 2 (1963) 111 MR146301
11 K Burns, R Spatzier, Manifolds of nonpositive curvature and their buildings, Inst. Hautes Études Sci. Publ. Math. 65 (1987) 35 MR908215
12 K Burns, R Spatzier, On topological Tits buildings and their classification, Inst. Hautes Études Sci. Publ. Math. 65 (1987) 5 MR908214
13 H Busemann, P J Kelly, Projective geometry and projective metrics, Academic (1953) MR0054980
14 D Cooper, D D Long, S Tillmann, On convex projective manifolds and cusps, Adv. Math. 277 (2015) 181 MR3336086
15 J Faraut, A Korányi, Analysis on symmetric cones, Clarendon (1994) MR1446489
16 W M Goldman, Convex real projective structures on compact surfaces, J. Differential Geom. 31 (1990) 791 MR1053346
17 P de la Harpe, On Hilbert’s metric for simplices, from: "Geometric group theory, I" (editors G A Niblo, M A Roller), London Math. Soc. Lecture Note Ser. 181, Cambridge Univ. Press (1993) 97 MR1238518
18 M Islam, Rank-one Hilbert geometries, preprint (2019) arXiv:1912.13013
19 M Islam, A Zimmer, A flat torus theorem for convex co-compact actions of projective linear groups, J. Lond. Math. Soc. 103 (2021) 470 MR4230908
20 G Knieper, The uniqueness of the measure of maximal entropy for geodesic flows on rank 1 manifolds, Ann. of Math. 148 (1998) 291 MR1652924
21 M Koecher, The Minnesota notes on Jordan algebras and their applications, 1710, Springer (1999) MR1718170
22 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
23 R D Nussbaum, Hilbert’s projective metric and iterated nonlinear maps, 391, Amer. Math. Soc. (1988) MR961211
24 G Prasad, M S Raghunathan, Cartan subgroups and lattices in semi-simple groups, Ann. of Math. 96 (1972) 296 MR302822
25 J F Quint, Convexes divisibles (d’après Yves Benoist), from: "Séminaire Bourbaki 2008/2009", Astérisque 332, Soc. Math. France (2010) 45 MR2648674
26 C Vernicos, On the Hilbert geometry of convex polytopes, from: "Handbook of Hilbert geometry" (editors A Papadopoulos, M Troyanov), IRMA Lect. Math. Theor. Phys. 22, Eur. Math. Soc. (2014) 111 MR3329878
27 J Vey, Sur les automorphismes affines des ouverts convexes saillants, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 24 (1970) 641 MR283720
28 È B Vinberg, The theory of homogeneous convex cones, Trudy Moskov. Mat. Obšč. 12 (1963) 303 MR0158414
29 È B Vinberg, Structure of the group of automorphisms of a homogeneous convex cone, Trudy Moskov. Mat. Obšč. 13 (1965) 56 MR0201575