Volume 22, issue 5 (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
Finsler bordifications of symmetric and certain locally symmetric spaces

Michael Kapovich and Bernhard Leeb

Geometry & Topology 22 (2018) 2533–2646
Bibliography
1 A Ash, D Mumford, M Rapoport, Y Tai, Smooth compactification of locally symmetric varieties, IV, Math. Sci. (1975) MR0457437
2 W L Baily Jr., A Borel, Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math. 84 (1966) 442 MR0216035
3 W Ballmann, Lectures on spaces of nonpositive curvature, 25, Birkhäuser (1995) MR1377265
4 W Ballmann, M Gromov, V Schroeder, Manifolds of nonpositive curvature, 61, Birkhäuser (1985) MR823981
5 Y Benoist, Propriétés asymptotiques des groupes linéaires, Geom. Funct. Anal. 7 (1997) 1 MR1437472
6 M Bestvina, G Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991) 469 MR1096169
7 A Borel, Linear algebraic groups, 126, Springer (1991) MR1102012
8 A Borel, L Ji, Compactifications of symmetric and locally symmetric spaces, Birkhäuser (2006) MR2189882
9 A Borel, J P Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973) 436 MR0387495
10 B H Bowditch, Geometrical finiteness for hyperbolic groups, J. Funct. Anal. 113 (1993) 245 MR1218098
11 B H Bowditch, Geometrical finiteness with variable negative curvature, Duke Math. J. 77 (1995) 229 MR1317633
12 B H Bowditch, A topological characterisation of hyperbolic groups, J. Amer. Math. Soc. 11 (1998) 643 MR1602069
13 B H Bowditch, Convergence groups and configuration spaces, from: "Geometric group theory down under" (editors J Cossey, W D Neumann, M Shapiro), de Gruyter (1999) 23 MR1714838
14 B Brill, Eine Familie von Kompaktifizierungen affiner Gebäude, dissertation, Goethe University Frankfurt (2006)
15 C Chevalley, Sur les décompositions cellulaires des espaces G∕B, from: "Algebraic groups and their generalizations: classical methods" (editors W J Haboush, B J Parshall), Proc. Sympos. Pure Math. 56, Amer. Math. Soc. (1994) 1 MR1278698
16 R J Daverman, Decompositions of manifolds, 124, Academic (1986) MR872468
17 P B Eberlein, Geometry of nonpositively curved manifolds, Univ. of Chicago Press (1996) MR1441541
18 C Frances, Lorentzian Kleinian groups, Comment. Math. Helv. 80 (2005) 883 MR2182704
19 H Furstenberg, A Poisson formula for semisimple Lie groups, Ann. of Math. 77 (1963) 335 MR0146298
20 F W Gehring, G J Martin, Discrete convergence groups, from: "Complex analysis, I" (editor C A Berenstein), Lecture Notes in Math. 1275, Springer (1987) 158 MR922298
21 M Gromov, Hyperbolic manifolds, groups and actions, from: "Riemann surfaces and related topics" (editors I Kra, B Maskit), Ann. of Math. Stud. 97, Princeton Univ. Press (1981) 183 MR624814
22 B Grünbaum, Convex polytopes, 221, Springer (2003) MR1976856
23 O Guichard, F Kassel, A Wienhard, Tameness of Riemannian locally symmetric spaces arising from Anosov representations, preprint (2015) arXiv:1508.04759
24 O Guichard, A Wienhard, Anosov representations: domains of discontinuity and applications, Invent. Math. 190 (2012) 357 MR2981818
25 L Ji, A S Schilling, Polyhedral horofunction compactification as polyhedral ball, preprint (2016) arXiv:1607.00564
26 D Joyce, D-manifolds, d-orbifolds and derived differential geometry: a detailed summary, preprint (2012) arXiv:1208.4948
27 M Kapovich, B Leeb, Discrete isometry groups of symmetric spaces, preprint (2017) arXiv:1703.02160
28 M Kapovich, B Leeb, J Millson, Convex functions on symmetric spaces, side lengths of polygons and the stability inequalities for weighted configurations at infinity, J. Differential Geom. 81 (2009) 297 MR2472176
29 M Kapovich, B Leeb, J Porti, Dynamics at infinity of regular discrete subgroups of isometries of higher rank symmetric spaces, preprint (2013) arXiv:1306.3837v1
30 M Kapovich, B Leeb, J Porti, Morse actions of discrete groups on symmetric space, preprint (2014) arXiv:1403.7671
31 M Kapovich, B Leeb, J Porti, A Morse lemma for quasigeodesics in symmetric spaces and euclidean buildings, preprint (2014) arXiv:1411.4176
32 M Kapovich, B Leeb, J Porti, Some recent results on Anosov representations, Transform. Groups 21 (2016) 1105 MR3569569
33 M Kapovich, B Leeb, J Porti, Anosov subgroups: dynamical and geometric characterizations, Eur. J. Math. 3 (2017) 808 MR3736790
34 M Kapovich, B Leeb, J Porti, Dynamics on flag manifolds: domains of proper discontinuity and cocompactness, Geom. Topol. 22 (2018) 157 MR3720343
35 A Karlsson, V Metz, G A Noskov, Horoballs in simplices and Minkowski spaces, Int. J. Math. Math. Sci. (2006) 1 MR2268510
36 F I Karpelevič, The geometry of geodesics and the eigenfunctions of the Beltrami–Laplace operator on symmetric spaces, Tr. Mosk. Mat. Obs. 14 (1965) 48 MR0231321
37 B Kleiner, B Leeb, Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, Inst. Hautes Études Sci. Publ. Math. 86 (1997) 115 MR1608566
38 B Kleiner, B Leeb, Rigidity of invariant convex sets in symmetric spaces, Invent. Math. 163 (2006) 657 MR2207236
39 F Labourie, Anosov flows, surface groups and curves in projective space, Invent. Math. 165 (2006) 51 MR2221137
40 A Marden, The geometry of finitely generated kleinian groups, Ann. of Math. 99 (1974) 383 MR0349992
41 J W Milnor, J D Stasheff, Characteristic classes, 76, Princeton Univ. Press (1974) MR0440554
42 S A Mitchell, Quillen’s theorem on buildings and the loops on a symmetric space, Enseign. Math. 34 (1988) 123 MR960196
43 S A Mitchell, Parabolic orbits in flag varieties, preprint (2008)
44 C C Moore, Compactifications of symmetric spaces, II : The Cartan domains, Amer. J. Math. 86 (1964) 358 MR0161943
45 A Parreau, La distance vectorielle dans les immeubles affines et les espaces symétriques, in preparation
46 J G Ratcliffe, Foundations of hyperbolic manifolds, 149, Springer (1994) MR1299730
47 I Satake, On compactifications of the quotient spaces for arithmetically defined discontinuous groups, Ann. of Math. 72 (1960) 555 MR0170356
48 I Satake, On representations and compactifications of symmetric Riemannian spaces, Ann. of Math. 71 (1960) 77 MR0118775
49 E H Spanier, Algebraic topology, McGraw-Hill (1966) MRMR0210112
50 P Tukia, Convergence groups and Gromov’s metric hyperbolic spaces, New Zealand J. Math. 23 (1994) 157 MR1313451
51 P Tukia, Conical limit points and uniform convergence groups, J. Reine Angew. Math. 501 (1998) 71 MR1637829
52 C Walsh, The horofunction boundary of finite-dimensional normed spaces, Math. Proc. Cambridge Philos. Soc. 142 (2007) 497 MR2329698
53 C Walsh, The horoboundary and isometry group of Thurston’s Lipschitz metric, from: "Handbook of Teichmüller theory, IV" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 19, Eur. Math. Soc. (2014) 327 MR3289705
54 G M Ziegler, Lectures on polytopes, 152, Springer (1995) MR1311028