Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: W. Ballmann
Title: Lectures on spaces of nonpositive curvature
Additional book information: Birkhäuser, Basel, 1995, vii+112 pp., ISBN 3-7643-5242-6, $39.95$

Authors: Martin R. Bridson and André Haefliger
Title: Metric spaces of non-positive curvature
Additional book information: Springer-Verlag, Berlin, 1999, xxi+643 pp., ISBN 3-540-64324-9, $109.00$

Author: Patrick B. Eberlein
Title: Geometry of nonpositively curved manifolds
Additional book information: University of Chicago Press, Chicago, 1996, vii+449 pp., ISBN 0-226-18198-7, $45.00$

References [Enhancements On Off] (What's this?)

    Werner Ballmann, Axial isometries of manifolds of nonpositive curvature, Math. Ann. 259 (1982), no. 1, 131-144. MR 83i:53068 Werner Ballmann, Nonpositively curved manifolds of higher rank, Ann. of Math. (2) 122 (1985), no. 3, 597-609. MR 87e:53059 W. Ballmann, Lectures on spaces of nonpositive curvature, Birkhäuser Verlag, Basel, 1995. MR 97a:53053 Werner Ballmann and Michael Brin, Orbihedra of nonpositive curvature, Inst. Hautes Études Sci. Publ. Math. (1995), no. 82, 169-209. MR 97i:53049 Werner Ballmann, Misha Brin, and Patrick Eberlein, Structure of manifolds of nonpositive curvature. I, Ann. of Math. (2) 122 (1985), no. 1, 171-203. MR 87c:58092a Werner Ballmann, Misha Brin, and Ralf Spatzier, Structure of manifolds of nonpositive curvature. II, Ann. of Math. (2) 122 (1985), no. 2, 205-235. MR 87c:58092b G. Besson, G. Courtois, and S. Gallot, Entropies et rigidités des espaces localement symétriques de courbure strictement négative, Geom. Funct. Anal. 5 (1995), no. 5, 731-799. MR 96i:58136 D. Burago, S. Ferleger, and A. Kononenko, Uniform estimates on the number of collisions in semi-dispersing billiards, Ann. of Math. (2) 147 (1998), no. 3, 695-708. MR 99f:58120 Mladen Bestvina and Geoffrey Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991), no. 3, 469-481. MR 93j:20076 Marc Burger and Shahar Mozes, Finitely presented simple groups and products of trees, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997), no. 7, 747-752. MR 98g:20041 Brian H. Bowditch, Cut points and canonical splittings of hyperbolic groups, Acta Math. 180 (1998), no. 2, 145-186. MR 99g:20069 Brian H. Bowditch, A topological characterisation of hyperbolic groups, J. Amer. Math. Soc. 11 (1998), no. 3, 643-667. MR 99c:20048 Marc Bourdon and Hervé Pajot, Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings, Proc. Amer. Math. Soc. 127 (1999), no. 8, 2315-2324. MR 99j:30024 Marc Bourdon and Hervé Pajot, Rigidity of quasi-isometries for some hyperbolic buildings, Comment. Math. Helv. 75 (2000), no. 4, 701-736. CMP 2001:05 Keith Burns and Ralf Spatzier, Manifolds of nonpositive curvature and their buildings, Inst. Hautes Études Sci. Publ. Math. (1987), no. 65, 35-59. MR 88g:53050 Richard D. Canary, Ends of hyperbolic $3$-manifolds, J. Amer. Math. Soc. 6 (1993), no. 1, 1-35. MR 93e:57019 Élie Cartan, Leçons sur la géométrie des espaces de Riemann, Éditions Jacques Gabay, Sceaux, 1946. CMP 93:04 Ruth M. Charney and Michael W. Davis, Strict hyperbolization, Topology 34 (1995), no. 2, 329-350. MR 95m:57034 Alain Connes, Mikhaïl Gromov, and Henri Moscovici, Conjecture de Novikov et fibrés presque plats, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), no. 5, 273-277. MR 91e:57041 Andrew Casson and Douglas Jungreis, Convergence groups and Seifert fibered $3$-manifolds, Invent. Math. 118 (1994), no. 3, 441-456. MR 96f:57011 Kevin Corlette, Archimedean superrigidity and hyperbolic geometry, Ann. of Math. (2) 135 (1992), no. 1, 165-182. MR 92m:57048 Christopher B. Croke, Rigidity for surfaces of nonpositive curvature, Comment. Math. Helv. 65 (1990), no. 1, 150-169. MR 91d:53056 Michael W. Davis and Tadeusz Januszkiewicz, Hyperbolization of polyhedra, J. Differential Geom. 34 (1991), no. 2, 347-388. MR 92h:57036 Patrick Eberlein, A canonical form for compact nonpositively curved manifolds whose fundamental groups have nontrivial center, Math. Ann. 260 (1982), no. 1, 23-29. MR 84h:53049 Patrick Eberlein and Jens Heber, A differential geometric characterization of symmetric spaces of higher rank, Inst. Hautes Études Sci. Publ. Math. (1990), no. 71, 33-44. MR 91j:53022 Alex Eskin, Quasi-isometric rigidity of nonuniform lattices in higher rank symmetric spaces, Journal of the American Mathematical Society 11 (1998), no. 2, 321-361. MR 98g:22005 F. T. Farrell and W. C. Hsiang, On Novikov's conjecture for nonpositively curved manifolds. I, Ann. of Math. (2) 113 (1981), no. 1, 199-209. MR 83j:57018 F. T. Farrell and L. E. Jones, Topological rigidity for compact non-positively curved manifolds, Differential geometry: Riemannian geometry (Los Angeles, CA, 1990), Amer. Math. Soc., Providence, RI, 1993, pp. 229-274. MR 94m:57067 David Gabai, Convergence groups are Fuchsian groups, Ann. of Math. (2) 136 (1992), no. 3, 447-510. MR 93m:20065 David Gabai, On the geometric and topological rigidity of hyperbolic $3$-manifolds, J. Amer. Math. Soc. 10 (1997), no. 1, 37-74. MR 97h:57028 D. Gabai, R. Meyerhoff, and N. Thurston, Homotopy hyperbolic 3-manifolds are hyperbolic, Annals of Math, to appear. M. Gromov, Hyperbolic groups, Essays in group theory, Springer, New York, 1987, pp. 75-263. MR 89e:20070 Mikhail Gromov and Richard Schoen, Harmonic maps into singular spaces and $p$-adic superrigidity for lattices in groups of rank one, Inst. Hautes Études Sci. Publ. Math. (1992), no. 76, 165-246. MR 94e:58032 Detlef Gromoll and Joseph A. Wolf, Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of nonpositive curvature, Bull. Amer. Math. Soc. 77 (1971), 545-552. MR 43:6841 Juha Heinonen and Pekka Koskela, Quasiconformal maps in metric spaces with controlled geometry, Acta Math. 181 (1998), no. 1, 1-61. MR 99j:30025 Michael Kapovich, Hyperbolic manifolds and discrete groups, Birkhäuser Boston Inc., Boston, MA, 2001. Michael Kapovich and Bernhard Leeb, Quasi-isometries preserve the geometric decomposition of Haken manifolds, Invent. Math. 128 (1997), no. 2, 393-416. MR 98k:57029 Bruce Kleiner and Bernhard Leeb, Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, Inst. Hautes Études Sci. Publ. Math. (1997), no. 86, 115-197 (1998). MR 98m:53068 Nicholas J. Korevaar and Richard M. Schoen, Sobolev spaces and harmonic maps for metric space targets, Comm. Anal. Geom. 1 (1993), no. 3-4, 561-659. MR 95b:58043 B. Leeb, A characterization of irreducible symmetric spaces and euclidean buildings of higher rank by their asymptotic geometry, Preprint, June, 1997. H. Blaine Lawson, Jr. and Shing Tung Yau, Compact manifolds of nonpositive curvature, J. Differential Geometry 7 (1972), 211-228. MR 48:12402 Curtis T. McMullen, Renormalization and 3-manifolds which fiber over the circle, Princeton University Press, Princeton, NJ, 1996. MR 97f:57022 Yair N. Minsky, On rigidity, limit sets, and end invariants of hyperbolic $3$-manifolds, J. Amer. Math. Soc. 7 (1994), no. 3, 539-588. MR 94m:57029 Yair N. Minsky, The classification of punctured-torus groups, Ann. of Math. (2) 149 (1999), no. 2, 559-626. MR 2000f:30028 G. D. Mostow, Strong rigidity of locally symmetric spaces, Princeton University Press, Princeton, N.J., 1973, Annals of Mathematics Studies, No. 78. MR 52:5874 John W. Morgan and Peter B. Shalen, Valuations, trees, and degenerations of hyperbolic structures. I, Ann. of Math. (2) 120 (1984), no. 3, 401-476. MR 86f:57011 Ngaiming Mok, Yum Tong Siu, and Sai-Kee Yeung, Geometric superrigidity, Invent. Math. 113 (1993), no. 1, 57-83. MR 94h:53079 Jean-Pierre Otal, Le spectre marqué des longueurs des surfaces à courbure négative, Ann. of Math. (2) 131 (1990), no. 1, 151-162. Jean-Pierre Otal, Le théorème d'hyperbolisation pour les variétés fibrées de dimension 3, Astérisque (1996), no. 235, x+159. MR 97e:57013 Jean-Pierre Otal, Thurston's hyperbolization of Haken manifolds, Surveys in differential geometry, Vol. III (Cambridge, MA, 1996), Int. Press, Boston, MA, 1998, pp. 77-194. MR 2000b:57025 Pierre Pansu, Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. (2) 129 (1989), no. 1, 1-60. MR 90e:53058 E. Rips and Z. Sela, Structure and rigidity in hyperbolic groups. I, Geom. Funct. Anal. 4 (1994), no. 3, 337-371. MR 96c:20067 Richard Schwartz, The quasi-isometry classification of rank one lattices, Inst. Hautes Études Sci. Publ. Math. 82 (1995), 133-168. MR 97c:22014 Z. Sela, The isomorphism problem for hyperbolic groups. I, Ann. of Math. (2) 141 (1995), no. 2, 217-283. MR 96b:20049

Review Information:

Reviewer: Bruce Kleiner
Affiliation: University of Michigan, Ann Arbor
Email: bkleiner@math.lsa.umich.edu
Journal: Bull. Amer. Math. Soc. 39 (2002), 273-279
Published electronically: January 4, 2002
Review copyright: © Copyright 2002 American Mathematical Society