Volume 20, issue 4 (2016)

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

Volume 30, 1 issue

Volume 29, 9 issues

Volume 28, 9 issues

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
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
Characterizing the unit ball by its projective automorphism group

Andrew M Zimmer

Geometry & Topology 20 (2016) 2397–2432
Bibliography
1 M Andersson, M Passare, R Sigurdsson, Complex convexity and analytic functionals, 225, Birkhäuser (2004) MR2060426
2 Y Benoist, Automorphismes des cônes convexes, Invent. Math. 141 (2000) 149 MR1767272
3 Y Benoist, Convexes divisibles, I, from: "Algebraic groups and arithmetic" (editors S G Dani, G Prasad), Tata Inst. Fund. Res. (2004) 339 MR2094116
4 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 Press (2008) 1 MR2464391
5 R Bowen, Hausdorff dimension of quasicircles, Inst. Hautes Études Sci. Publ. Math. 50 (1979) 11 MR556580
6 A Cano, J Seade, On discrete groups of automorphisms of 2, Geom. Dedicata 168 (2014) 9 MR3158029
7 B Colbois, P Verovic, Rigidity of Hilbert metrics, Bull. Austral. Math. Soc. 65 (2002) 23 MR1889375
8 T tom Dieck, Algebraic topology, European Mathematical Society (2008) MR2456045
9 L Dubois, Projective metrics and contraction principles for complex cones, J. Lond. Math. Soc. 79 (2009) 719 MR2506695
10 S Frankel, Complex geometry of convex domains that cover varieties, Acta Math. 163 (1989) 109 MR1007621
11 W M Goldman, Convex real projective structures on compact surfaces, J. Differential Geom. 31 (1990) 791 MR1053346
12 W M Goldman, Projective geometry on manifolds, preprint (2009)
13 L Hörmander, Notions of convexity, 127, Birkhäuser (1994) MR1301332
14 A V Isaev, S G Krantz, Domains with non-compact automorphism group: a survey, Adv. Math. 146 (1999) 1 MR1706680
15 K Jo, A rigidity result for domains with a locally strictly convex point, Adv. Geom. 8 (2008) 315 MR2427461
16 M Kapovich, Convex projective structures on Gromov–Thurston manifolds, Geom. Topol. 11 (2007) 1777 MR2350468
17 S Kobayashi, Intrinsic distances associated with flat affine or projective structures, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24 (1977) 129 MR0445016
18 S Kobayashi, T Ochiai, Holomorphic projective structures on compact complex surfaces, Math. Ann. 249 (1980) 75 MR575449
19 S G Krantz, The impact of the theorem of Bun Wong and Rosay, Complex Var. Elliptic Equ. 59 (2014) 966 MR3195923
20 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
21 G D Mostow, Strong rigidity of locally symmetric spaces, 78, Princeton Univ. Press (1973) MR0385004
22 J F Quint, Convexes divisibles (d’après Yves Benoist), from: "Séminaire Bourbaki, Volume 2008/2009", Astérisque 332, Société Mathématique de France (2010) 45 MR2648674
23 J P Rosay, Sur une caractérisation de la boule parmi les domaines de Cn par son groupe d’automorphismes, Ann. Inst. Fourier (Grenoble) 29 (1979) 91 MR558590
24 E Socié-Méthou, Caractérisation des ellipsoïdes par leurs groupes d’automorphismes, Ann. Sci. École Norm. Sup. 35 (2002) 537 MR1981171
25 S M Webster, On the mapping problem for algebraic real hypersurfaces, Invent. Math. 43 (1977) 53 MR0463482
26 B Wong, Characterization of the unit ball in Cn by its automorphism group, Invent. Math. 41 (1977) 253 MR0492401
27 C Yi, Projective domains with non-compact automorphism groups, I, J. Korean Math. Soc. 45 (2008) 1221 MR2439731
28 A M Zimmer, Rigidity of complex convex divisible sets, preprint (2013) arXiv:1308.4116
29 A M Zimmer, Characterizing polynomial domains by their automorphism group, preprint (2015) arXiv:1506.07852
30 A M Zimmer, Proper quasi-homogeneous domains in flag manifolds and geometric structures, preprint (2015) arXiv:1507.06921