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References
[Ale] A.D. Aleksandrov, Convex Polytopes, Moscow 1950 (Russian).
[And] E. Andreev, Convex polyhedra of finite volume in Lobachevski space (Russian), Mat. Sb. 83 (125) (1970) p.p. 256–260.
[Bas] H. Bass, The congruence subgroup problem, Proc. Conf. Local Fields, Driebergen 1966, Springer 1967, p.p. 16–22.
[B-G-S] W. Ballmann, M. Gromov, V. Schroeder, Manifolds of non-positive curvature. Progress in Math. Vol. 61. Birkhäuser, Boston-Basel-Stuttgart (1985).
[Bes] A.L. Besse, Einstein manifolds, Ergeb. Bd. 10, Springer Verlag, 1986.
[Bor]1 A. Borel, Introduction aux groupes arithmétiques, Hermann, Paris 1969.
[Bor]2 A. Borel, Compact Clifford-Klein forms of symmetric spaces, Topology 2, (1963), p.p. 111–122.
[Bor-Sha]Z.I. Borević and I.R. Shafareviĉ, Number theory, Acad. Press 1966.
[Bus] H. Buseman, Extremals on closed hyperbolic space forms, Tensor, 16 (1965), p.p. 313–318.
[B-Y] S. Bochner and K. Jano, Curvature and Betti numbers, Princeton University Press, Princeton 1953.
[Cal] E. Calabi, On compact Riemannian manifolds with constant curvature I. Proc. Symp. Pure Math. Vol III, p.p. 155–180, A.M.S., Providence, R.I. 1961.
[Cal-Ves] E. Calabi and E. Vesentini, On compact locally symmetric Kähler manifolds, Ann. of Math. (2) 71 (1960), p.p. 472–507.
[Car-Tol] J. Carlson, D. Toledo, Harmonic maps of Kähler manifolds to locally symmetric spaces, Publ. Math. I.H.E.S. 69 (1989), p.p. 173–201.
[Cas] J.W.S. Cassels, An introduction to the geometry of numbers, Springer-Verlag 1959.
[Ch-Eb] F. Cheeger, D. Ebin, Comparison theorems in Riemannian geometry, North-Holland 1975.
[Che] S.S. Chern, On a generalization of Kähler geometry, in “Algebraic Geometry and Topology Symp. in honor of S. Lefschetz”, Princeton Univ. Press, (1957), p.p. 103–121.
[Cor]1 K. Corlette, Archimedean superrigidity and hyperbolic geometry, preprint 1990.
[Cor]2 K. Corlette, Flat G-bundles and canonical metrics, J. Diff. Geom. 28 (1988), p.p. 361–382.
[dlH-V] P. de la Harpe et A. Valette. La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque 175 (1989). Soc. Math. de France.
[Don] S. Donaldson Twisted harmonic maps and the self duality equations, Proc. London Math. Soc. 55 (1987), p.p. 127–131.
[E-L]1 J. Eells and L. Lemaire, A report on harmonic maps, Bull. Lond. Math. Soc. 10 (1978), p.p. 1–68.
[E-L]2 J. Eells and L. Lemaire, Another report on harmonic maps, Bull. Lond. Math. Soc. 20 (1988), p.p. 385–525.
[E-S] J. Eells and J.H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), pp. 109–160.
[Efz] V. Efremoviĉ, The proximity geometry of Riemannian manifolds, Uspehi Mat., Nauk 8 (1953), p. 189 (Russian).
[Ef-Ti] V. Efremoviĉ and E. Tichomirova, Equimorphisms of hyperbolic spaces, Isv. Ac. Nauk. 28 (1964), p.p. 1139–1144.
[Fl] W. J. Floyd, Group completion and limit sets of Kleinian groups, Inv. Math. 57 (1980), p.p. 205–218.
[Für]1 H. Fürstenberg, Poisson boundaries and envelopes of discrete groups, Bull. Am. Math. Soc. 73 (1967), p.p. 350–356.
[Für]2 H. Fürstenberg, Rigidity and cocycles for ergodic actions of semisimple Lie groups. Lect. Notes Math. 842, p.p. 273–292, Springer-Verlag 1981.
[Für]3 H. Fürstenberg, Boundary theory and stochastic processes on homogeneous spaces. Proc. Symp. Pure Math. XXVI, 1973, p.p. 193–233.
[Geh] F.W. Gehring, Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc. 103 (1962), p.p. 353–393.
[Gro]1 M. Gromov, Hyperbolic manifolds according to Thurston and Jorgensen, in Springer Lecture Notes, 842 (1981), p.p. 40–53.
[Gro]2 M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. IHES, 53 (1981), p.p. 53–78.
[Gro]3 M. Gromov, Hyperbolic manifolds groups and actions, in Riem. surfaces and related topics, Ann. Math. Studies 97 (1981), p.p. 183–215.
[Gro]4 M. Gromov, Hyperbolic groups, in Essays in group theory, S.M. Gersten ed., p.p. 75–265, Springer-Verlag 1987.
[G-L-P] M. Gromov, J. Lafontaine, and P. Pansu, Structures métriques pour les variétés riemanniennes, CEDIC-Fernand Nathan, Paris, 1981.
[G-P] M. Gromov and I. Piatetski-Shapiro Non-arithmetic groups in Lobachevsky spaces, Publ. Math. I.H.E.S. 66 (1988), p.p. 93–103.
[G-S] M. Gromov, R. Schoen, in preparation.
[Ha-Mu] U. Haagerup and M. Munkholm, Simplices of maximal volume in hyperbolic n-space. Act. Math. 1941 (1981), p.p. 1–11.
[Hit] N. Hitchin, The selfduality equations on a Riemann surface, Proc. London Math. Soc. 55 (1987), p.p. 59–126.
[Kar] H. Karcher, Riemannian center of mass and mollifier smoothing, Comm. Pure and Appl. Math. 30 (1977), p.p. 509–541.
[Klin] W. Klingenberg, Geodätischer Fluss auf Mannigfaltigkeiten vom hyperbolischen Typ, Inv. Math. 14 (1971), p.p. 63–82.
[Law-Mic] B. Lawson and M.-L. Michelsohn, Spin geometry, Princeton University Press, Princeton 1989.
[Kaz] D. Kazhdan, Connection of the dual space of a group with the structure of its closed subgroups. Func. Anal. and Appl. 1 (1967), p.p. 63–65.
[Mal] A.I. Malcev, On a class of homogeneous spaces, Amer. Math. Soc. Transl 39, (1951), p.p. 276–307.
[Mar]1 G. Margulis, Discrete groups of motions of manifolds of non-positive curvature (Russian), ICM 1974. Translated in A.M.S. Transl. (2) 109 (1977), p.p. 33–45.
[Mar]2 G. Margulis, Discrete subgroups of semisimple Lie groups, Springer-Verlag 1990.
[Mar]3 G. Margulis, The isometry of closed manifolds of constant negative curvature with the same fundamental group, Dokl. Akad. Nauk. SSSR 192 (1970), p.p. 736–737.
[Mau] F.I. Mautner, Geodesic flows on symmetric Riemannian spaces, Ann. of Math. 65 (1957), p.p. 416–431.
[Mil]1 J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), p.p. 358–426.
[Mil]2 J. Milnor, A note on curvature and fundamental group, J. Diff. Geom. 2 (1968), p.p. 1–7.
[Mok] N. Mok, Metric rigidity theorems on Hermitian locally symmetric manifolds, World Sci. Singapore-New Jersey-London-Hong Kong, 1989.
[Mors] M. Morse, Geodesics on negatively curved surfaces, Trans. Amer. Math. Soc. 22 (1921), p.p. 84–100.
[Mos]1 G. Mostow, Quasi-conformal mappings in n-space and the rigidity of hyperbolic space form, Publ. Math. I.H.E.S., vol. 34, 1968, p.p. 53–104.
[Mos]2 G. Mostow, Equivariant embeddings in Euclidean space, Ann. of Math. 65 (1957), 432–446.
[Mos]3 G. Mostow, Factor spaces of solvable groups, Ann. of Math. 60 (1954), p.p. 1–27.
[Mos]4 G.D. Mostow, Strong rigidity of symmetric spaces, Ann. Math. Studies 78, Princeton 1973.
[Mos]5 G.D. Mostow, Some new decomposition theorems for semisimple groups, Memoirs Amer. Math. Soc. 14 (1955), p.p. 31–54.
[Pal] R. Palais, Equivalence of nearby differentiable actions of a compact group, Bull. Am. Math. Soc. 61 (1961), p.p. 362–364.
[Pan]1 P. Pansu, Croissance des boules et des géodésiques fermées dans les nilvariétés, Ergod. Th. Dynam. Syst. 3 (1983), p.p. 415–445.
[Pan]2 P. Pansu, Métriques de Carnot-Caratheodory et quasi-isométries des espaces symétriques de rang un, Ann. of Math. 129:1 (1989), p.p. 1–61.
[Pont] L.S. Pontryagin, Topological groups, Gordon and Breach 1966.
[Pra] G. Prasad, Strong rigidity of Q-rank 1 lattices, Inv. Math. 21 (1973), p.p. 255–286.
[Rag] M.S. Raghunathan, Discrete subgroups of Lie groups, Springer-Verlag, 1972.
[Resh] Yu. G. Reshetniak, On conformal mappings of a space, Dokl. Acad. Nauk. SSSR 130 (1960) p.p. 981–983=Soviet. Math. Dokl. 1 (1960), p.p. 122–124.
[Rei] H.M. Reimann, Capacities in the Heisenberg group, Preprint University of Bern (1987).
[Sel] A. Selberg, On discontinuous groups in higher dimensional symmetric spaces, Contribution to Function Theory, Tata Inst., Bombay 1960, p.p. 147–164.
[Sha] I. R. Shafareviĉ, Basic Algebraic geometry, Springer-Verlag 1974.
[Sam] J.H. Sampson, Applications of harmonic maps to Kähler geometry, Contemp. Math. 49 (1986). p.p. 125–133.
[Sim] C. Simpson, Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization, J. of the Amer. Math. Soc. 1 (1988), p.p. 867–918.
[Siu] Y.-T. Siu, The complex analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds, Ann. of Math. 112 (1980), p.p. 73–111.
[Str] R. Strichartz, Sub-Riemannian geometry, Journ. of Diff. Geom. 24, (1986), p.p. 221–263.
[Ŝv] A. Ŝvarc, A volume invariant of coverings, Dokl. Akad. Nauk SSSR 105 (1955), p.p. 32–34.
[Th] W. Thurston, Geometry and topology of 3-manifolds, Lecture notes Princeton, 1978.
[Tuk] P. Tukia, Quasiconformal extension of quasisymmetric maps compatible with a Möbius group, Acta Math. 154 (1985), p.p. 153–193.
[Tuk-Väi] P. Tukia, J. Väisälä, A remark on 1-quasiconformal maps, Ann. Acad. Sci. Fenn. 10 (1985), p.p. 561–562.
[Ul] S.M. Ulam, A collection of mathematical problems. Interscience Publ. N.Y. 1960.
[Väi] J. Väisälä, Lectures on n-dimensional quasiconformal mappings, Lecture Notes in Math. Vol 129, Springer, Berlin (1971).
[Wang] H.-C. Wang, Topics on totally discontinuous groups, in “Symmetric spaces” edited by W.M. Boothby and G.L. Weiss, p.p. 459–487, Marcel Dekker, Inc. N.Y. 1972.
[Wei] H. Weil, On discrete subgroups of Lie groups II, Ann. of Math. vol. 75 (1962), p.p. 578–602. *** DIRECT SUPPORT *** A00J4422 00003
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Gromov, M., Pansu, P. (1991). Rigidity of lattices: An introduction. In: de Bartolomeis, P., Tricerri, F. (eds) Geometric Topology: Recent Developments. Lecture Notes in Mathematics, vol 1504. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094289
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