Kleiner, Bruce; Leeb, Bernhard
Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings
Publications Mathématiques de l'IHÉS, Tome 86 (1997) , p. 115-197
Zbl 0910.53035 | MR 98m:53068 | 3 citations dans Numdam
URL stable : http://www.numdam.org/item?id=PMIHES_1997__86__115_0


[ABN] A. D. Aleksandrov, V. N. Berestovskij, I. G. Nikolaev, Generalized Riemannian Spaces, Russ. Math. Surveys 41, no. 3 (1986), 1-54. MR 88e:53103 | Zbl 0625.53059

[AS] M. T. Anderson and V. Schroeder, Existence of flats in manifolds of nonpositive curvature, Invent. Math. 85 (1986), no. 2, 303-315. MR 87h:53049 | Zbl 0615.53030

[Ba] W. Ballmann, Lectures on spaces of nonpositive curvature, preprint 1995. MR 97a:53053 | Zbl 0834.53003

[BGS] W. Ballmann, M. Gromov, V. Schroeder, Manifolds of nonpositive curvature, Birkhäuser, 1985. MR 87h:53050 | Zbl 0591.53001

[Brbk] N. Bourbaki, Groupes et Algèbres de Lie, ch. 4-6, Paris, Masson, 1981. Zbl 0483.22001

[Brn1] K. Brown, Buildings, Springer, 1989. MR 90e:20001 | Zbl 0715.20017

[Brn2] K. Brown, Five lectures on Buildings, p. 254-295, in Group theory from a geometric viewpoint, Trieste, 1990. MR 94b:51017 | Zbl 0846.20032

[BT] F. Bruhat and J. Tits, Groupes réductifs sur un corps local, Publ. Math. IHES 60 (1984), 5-184. Numdam | MR 86c:20042 | Zbl 0597.14041

[ChE] J. Cheeger and D. Ebin, Comparison theorems in Riemannian geometry, North Holland, 1975. MR 56 #16538 | Zbl 0309.53035

[DW] L. Van Den Dries, A. J. Wilkie, On Gromov's Theorem concerning groups of polynomial growth and elementary logic, J. of Algebra 89 (1984), 349-374. MR 85k:20101 | Zbl 0552.20017

[Eb] P. Eberlein, Structure of manifolds of nonpositive curvature, in Springer LNM, vol. 1156 (1985), 86-153. MR 87d:53080 | Zbl 0569.53020

[Gro] M. Gromov, Asymptotic invariants for infinite groups, in Geometric group theory, London Math. Soc. Lecture Notes Series 182 (1993), vol. 2. MR 95m:20041 | Zbl 0841.20039

[GrPa] M. Gromov and P. Pansu, Rigidity of lattices : An introduction, in Geometric Topology : Recent developments, Springer LNM 1504 (1991), 39-137. MR 93f:53036 | Zbl 0786.22015

[GrBe] L. C. Grove and C. T. Benson, Finite reflection groups, Springer GTM 99, sec. ed., 1985. MR 85m:20001 | Zbl 0579.20045

[Hum] J. E. Humphreys, Reflection groups and Coxeter groups, Cambridge studies in advanced mathematics 29, Cambridge Univ. Press, 1990. MR 92h:20002 | Zbl 0725.20028

[KKL] M. Kapovich, B. Kleiner and B. Leeb, Quasi-isometries preserve the de Rham decomposition, to appear in Topology. Zbl 0954.53027

[KaLe] M. Kapovich and B. Leeb, Asymptotic cones and quasi-isometry classes of fundamental groups of 3-manifolds, GAFA, vol. 5, no. 3 (1995), 582-603. MR 96e:57006 | Zbl 0829.57006

[KlLe1] B. Kleiner and B. Leeb, Rigidity of quasi-isometries for symmetric spaces of higher rank, Preprint, January 1995.

[KlLe2] B. Kleiner and B. Leeb, Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, C. R. Acad. Sci. Paris, Série I, 324 (1997), 639-643. MR 98f:53046 | Zbl 0882.53037

[KlLe3] B. Kleiner and B. Leeb, Groups quasi-isometric to symmetric spaces, Preprint, October 1996. Zbl 01652733

[Le] B. Leeb, A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry, Habilitationsschrift, Universität Bonn, Juni 1997. Zbl 01620191

[Mos] G. D. Mostow, Strong rigidity of locally symmetric spaces, Ann. of Math. Studies, vol. 78, 1973. MR 52 #5874 | Zbl 0265.53039

[Nik] I. Nikolaev, The tangent cone of an Aleksandrov space of curvature ≤ K, to appear in Manuscripta Mathematica. Zbl 0822.53043

[Pan] P. Pansu, Métriques de Carnot-Carathéodory et quasi-isométries des espaces symétriques de rang un, Ann. of Math. 129 (1989), 1-60. MR 90e:53058 | Zbl 0678.53042

[Ron] M. Ronan, Lectures on Buildings, Perspectives in Mathematics, vol. 7, Academic Press, 1989. MR 90j:20001 | Zbl 0694.51001

[Sch] R. Schwartz, Quasi-Isometric Rigidity and Diophantine Approximation, Acta Mathematica 177 (1996), 75-112. MR 97m:53093 | Zbl 1029.11038

[Ti1] J. Tits, Buildings of spherical type and finite BN-pairs, Springer LNM, vol. 386 (1974). MR 57 #9866 | Zbl 0295.20047

[Ti2] J. Tits, Immeubles de type affine, in Buildings and the geometry of diagrams, Proceedings Como, 1984, Springer LNM, vol. 1181 (1986), 159-190. MR 87h:20077 | Zbl 0611.20026

[Thu] W. Thurston, The geometry and topology of 3-manifolds, Lecture notes, Princeton University, 1979.

[Tuk] P. Tukia, Quasiconformal extension of quasisymmetric mappings compatible with a Möbius group, Acta. Math. 154 (1985), 153-193. MR 86f:30024 | Zbl 0562.30018