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

Volume 30
Issue 5, 1611–2042
Issue 4, 1203–1610
Issue 3, 835–1201
Issue 2, 389–833
Issue 1, 1–388

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
Discrete subgroups with finite Bowen–Margulis–Sullivan measure in higher rank

Mikołaj Frączyk and Minju Lee

Geometry & Topology 29 (2025) 1017–1036
Bibliography
1 Y Benoist, Propriétés asymptotiques des groupes linéaires, Geom. Funct. Anal. 7 (1997) 1 MR1437472
2 J Bochi, R Potrie, A Sambarino, Anosov representations and dominated splittings, J. Eur. Math. Soc. 21 (2019) 3343 MR4012341
3 M Bridgeman, R Canary, F Labourie, A Sambarino, The pressure metric for Anosov representations, Geom. Funct. Anal. 25 (2015) 1089 MR3385630
4 M Burger, O Landesberg, M Lee, H Oh, The Hopf–Tsuji–Sullivan dichotomy in higher rank and applications to Anosov subgroups, J. Mod. Dyn. 19 (2023) 301 MR4588419
5 F Dal’bo, J P Otal, M Peigné, Séries de Poincaré des groupes géométriquement finis, Israel J. Math. 118 (2000) 109 MR1776078
6 S Edwards, M Fraczyk, M Lee, H Oh, Infinite volume and atoms at the bottom of the spectrum, C. R. Math. Acad. Sci. Paris 362 (2024) 1873 MR4834589
7 S Edwards, M Lee, H Oh, Anosov groups: local mixing, counting and equidistribution, Geom. Topol. 27 (2023) 513 MR4589560
8 S Edwards, H Oh, Temperedness of L2 G) and positive eigenfunctions in higher rank, Commun. Am. Math. Soc. 3 (2023) 744 MR4646249
9 M Einsiedler, A Katok, Invariant measures on G∕Γ for split simple Lie groups G, Comm. Pure Appl. Math. 56 (2003) 1184 MR1989231
10 M Einsiedler, A Katok, E Lindenstrauss, Invariant measures and the set of exceptions to Littlewood’s conjecture, Ann. of Math. 164 (2006) 513 MR2247967
11 M Einsiedler, E Lindenstrauss, Diagonal actions on locally homogeneous spaces, from: "Homogeneous flows, moduli spaces and arithmetic", Clay Math. Proc. 10, Amer. Math. Soc. (2010) 155 MR2648695
12 V Fock, A Goncharov, Moduli spaces of local systems and higher Teichmüller theory, Publ. Math. Inst. Hautes Études Sci. 103 (2006) 1 MR2233852
13 M Fraczyk, T Gelander, Infinite volume and infinite injectivity radius, Ann. of Math. 197 (2023) 389 MR4515682
14 F Guéritaud, O Guichard, F Kassel, A Wienhard, Anosov representations and proper actions, Geom. Topol. 21 (2017) 485 MR3608719
15 O Guichard, A Wienhard, Anosov representations: domains of discontinuity and applications, Invent. Math. 190 (2012) 357 MR2981818
16 N J Hitchin, Lie groups and Teichmüller space, Topology 31 (1992) 449 MR1174252
17 M Kapovich, B Leeb, J Porti, Anosov subgroups: dynamical and geometric characterizations, Eur. J. Math. 3 (2017) 808 MR3736790
18 F Kassel, Geometric structures and representations of discrete groups, from: "Proceedings of the International Congress of Mathematicians, II", World Sci. (2018) 1115 MR3966802
19 B Kleiner, B Leeb, Rigidity of invariant convex sets in symmetric spaces, Invent. Math. 163 (2006) 657 MR2207236
20 F Labourie, Anosov flows, surface groups and curves in projective space, Invent. Math. 165 (2006) 51 MR2221137
21 G A Margulis, Certain measures associated with U-flows on compact manifolds, Funkcional. Anal. i Priložen. 4 (1970) 62 MR272984
22 S J Patterson, The limit set of a Fuchsian group, Acta Math. 136 (1976) 241 MR450547
23 Y B Pesin, Characteristic Lyapunov exponents and smooth ergodic theory, Uspehi Mat. Nauk 32 (1977) 55 MR466791
24 J F Quint, Divergence exponentielle des sous-groupes discrets en rang supérieur, Comment. Math. Helv. 77 (2002) 563 MR1933790
25 J F Quint, Mesures de Patterson–Sullivan en rang supérieur, Geom. Funct. Anal. 12 (2002) 776 MR1935549
26 J F Quint, Groupes convexes cocompacts en rang supérieur, Geom. Dedicata 113 (2005) 1 MR2171296
27 D Sullivan, The density at infinity of a discrete group of hyperbolic motions, Inst. Hautes Études Sci. Publ. Math. 50 (1979) 171 MR556586
28 A Wienhard, An invitation to higher Teichmüller theory, from: "Proceedings of the International Congress of Mathematicians, II", World Sci. (2018) 1013 MR3966798