Bulletin of the American Mathematical Society

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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, $45.00$

[Bal82]

Werner Ballmann, Axial isometries of manifolds of nonpositive curvature, Math. Ann. 259 (1982), no. 1, 131-144. MR 83i:53068

[Bal85]

Werner Ballmann, Nonpositively curved manifolds of higher rank, Ann. of Math. (2) 122 (1985), no. 3, 597-609. MR 87e:53059

[Bal95]

W. Ballmann, Lectures on spaces of nonpositive curvature, Birkhäuser Verlag, Basel, 1995. MR 97a:53053

[BB95]

Werner Ballmann and Michael Brin, Orbihedra of nonpositive curvature, Inst. Hautes Études Sci. Publ. Math. (1995), no. 82, 169-209. MR 97i:53049

[BBE85]

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

[BBS85]

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

[BCG95]

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

[BFK98]

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

[BM91]

Mladen Bestvina and Geoffrey Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991), no. 3, 469-481. MR 93j:20076

[BM97]

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

[Bow98a]

Brian H. Bowditch, Cut points and canonical splittings of hyperbolic groups, Acta Math. 180 (1998), no. 2, 145-186. MR 99g:20069

[Bow98b]

Brian H. Bowditch, A topological characterisation of hyperbolic groups, J. Amer. Math. Soc. 11 (1998), no. 3, 643-667. MR 99c:20048

[BP99]

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

[BP00]

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

[BS87]

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

[Can93]

Richard D. Canary, Ends of hyperbolic -manifolds, J. Amer. Math. Soc. 6 (1993), no. 1, 1-35. MR 93e:57019

[Car46]

Élie Cartan, Leçons sur la géométrie des espaces de Riemann, Éditions Jacques Gabay, Sceaux, 1946. CMP 93:04

[CD95]

Ruth M. Charney and Michael W. Davis, Strict hyperbolization, Topology 34 (1995), no. 2, 329-350. MR 95m:57034

[CGM90]

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

[CJ94]

Andrew Casson and Douglas Jungreis, Convergence groups and Seifert fibered -manifolds, Invent. Math. 118 (1994), no. 3, 441-456. MR 96f:57011

[Cor92]

Kevin Corlette, Archimedean superrigidity and hyperbolic geometry, Ann. of Math. (2) 135 (1992), no. 1, 165-182. MR 92m:57048

[Cro90]

Christopher B. Croke, Rigidity for surfaces of nonpositive curvature, Comment. Math. Helv. 65 (1990), no. 1, 150-169. MR 91d:53056

[DJ91]

Michael W. Davis and Tadeusz Januszkiewicz, Hyperbolization of polyhedra, J. Differential Geom. 34 (1991), no. 2, 347-388. MR 92h:57036

[Ebe82]

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

[EH90]

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

[Esk98]

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

[FH81]

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

[FJ93]

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

[Gab92]

David Gabai, Convergence groups are Fuchsian groups, Ann. of Math. (2) 136 (1992), no. 3, 447-510. MR 93m:20065

[Gab97]

David Gabai, On the geometric and topological rigidity of hyperbolic -manifolds, J. Amer. Math. Soc. 10 (1997), no. 1, 37-74. MR 97h:57028

[GMT]

D. Gabai, R. Meyerhoff, and N. Thurston, Homotopy hyperbolic 3-manifolds are hyperbolic, Annals of Math, to appear.

[Gro87]

M. Gromov, Hyperbolic groups, Essays in group theory, Springer, New York, 1987, pp. 75-263. MR 89e:20070

[GS92]

Mikhail Gromov and Richard Schoen, Harmonic maps into singular spaces and -adic superrigidity for lattices in groups of rank one, Inst. Hautes Études Sci. Publ. Math. (1992), no. 76, 165-246. MR 94e:58032

[GW71]

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

[HK98]

Juha Heinonen and Pekka Koskela, Quasiconformal maps in metric spaces with controlled geometry, Acta Math. 181 (1998), no. 1, 1-61. MR 99j:30025

[Kap01]

Michael Kapovich, Hyperbolic manifolds and discrete groups, Birkhäuser Boston Inc., Boston, MA, 2001.

[KL97a]

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

[KL97b]

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

[KS93]

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

[Lee97]

B. Leeb, A characterization of irreducible symmetric spaces and euclidean buildings of higher rank by their asymptotic geometry, Preprint, June, 1997.

[LY72]

H. Blaine Lawson, Jr. and Shing Tung Yau, Compact manifolds of nonpositive curvature, J. Differential Geometry 7 (1972), 211-228. MR 48:12402

[McM96]

Curtis T. McMullen, Renormalization and 3-manifolds which fiber over the circle, Princeton University Press, Princeton, NJ, 1996. MR 97f:57022

[Min94]

Yair N. Minsky, On rigidity, limit sets, and end invariants of hyperbolic -manifolds, J. Amer. Math. Soc. 7 (1994), no. 3, 539-588. MR 94m:57029

[Min99]

Yair N. Minsky, The classification of punctured-torus groups, Ann. of Math. (2) 149 (1999), no. 2, 559-626. MR 2000f:30028

[Mos73]

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

[MS84]

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

[MSY93]

Ngaiming Mok, Yum Tong Siu, and Sai-Kee Yeung, Geometric superrigidity, Invent. Math. 113 (1993), no. 1, 57-83. MR 94h:53079

[Ota90]

Jean-Pierre Otal, Le spectre marqué des longueurs des surfaces à courbure négative, Ann. of Math. (2) 131 (1990), no. 1, 151-162.

[Ota96]

Jean-Pierre Otal, Le théorème d'hyperbolisation pour les variétés fibrées de dimension 3, Astérisque (1996), no. 235, x+159. MR 97e:57013

[Ota98]

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

[Pan89]

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

[RS94]

E. Rips and Z. Sela, Structure and rigidity in hyperbolic groups. I, Geom. Funct. Anal. 4 (1994), no. 3, 337-371. MR 96c:20067

[Sch95]

Richard Schwartz, The quasi-isometry classification of rank one lattices, Inst. Hautes Études Sci. Publ. Math. 82 (1995), 133-168. MR 97c:22014

[Sel95]

Z. Sela, The isomorphism problem for hyperbolic groups. I, Ann. of Math. (2) 141 (1995), no. 2, 217-283. MR 96b:20049

[Bal82]

Werner Ballmann, Axial isometries of manifolds of nonpositive curvature, Math. Ann. 259 (1982), no. 1, 131-144. MR 83i:53068

[Bal85]

Werner Ballmann, Nonpositively curved manifolds of higher rank, Ann. of Math. (2) 122 (1985), no. 3, 597-609. MR 87e:53059

[Bal95]

W. Ballmann, Lectures on spaces of nonpositive curvature, Birkhäuser Verlag, Basel, 1995. MR 97a:53053

[BB95]

Werner Ballmann and Michael Brin, Orbihedra of nonpositive curvature, Inst. Hautes Études Sci. Publ. Math. (1995), no. 82, 169-209. MR 97i:53049

[BBE85]

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

[BBS85]

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

[BCG95]

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

[BFK98]

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

[BM91]

Mladen Bestvina and Geoffrey Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991), no. 3, 469-481. MR 93j:20076

[BM97]

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

[Bow98a]

Brian H. Bowditch, Cut points and canonical splittings of hyperbolic groups, Acta Math. 180 (1998), no. 2, 145-186. MR 99g:20069

[Bow98b]

Brian H. Bowditch, A topological characterisation of hyperbolic groups, J. Amer. Math. Soc. 11 (1998), no. 3, 643-667. MR 99c:20048

[BP99]

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

[BP00]

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

[BS87]

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

[Can93]

Richard D. Canary, Ends of hyperbolic -manifolds, J. Amer. Math. Soc. 6 (1993), no. 1, 1-35. MR 93e:57019

[Car46]

Élie Cartan, Leçons sur la géométrie des espaces de Riemann, Éditions Jacques Gabay, Sceaux, 1946. CMP 93:04

[CD95]

Ruth M. Charney and Michael W. Davis, Strict hyperbolization, Topology 34 (1995), no. 2, 329-350. MR 95m:57034

[CGM90]

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

[CJ94]

Andrew Casson and Douglas Jungreis, Convergence groups and Seifert fibered -manifolds, Invent. Math. 118 (1994), no. 3, 441-456. MR 96f:57011

[Cor92]

Kevin Corlette, Archimedean superrigidity and hyperbolic geometry, Ann. of Math. (2) 135 (1992), no. 1, 165-182. MR 92m:57048

[Cro90]

Christopher B. Croke, Rigidity for surfaces of nonpositive curvature, Comment. Math. Helv. 65 (1990), no. 1, 150-169. MR 91d:53056

[DJ91]

Michael W. Davis and Tadeusz Januszkiewicz, Hyperbolization of polyhedra, J. Differential Geom. 34 (1991), no. 2, 347-388. MR 92h:57036

[Ebe82]

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

[EH90]

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

[Esk98]

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

[FH81]

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

[FJ93]

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

[Gab92]

David Gabai, Convergence groups are Fuchsian groups, Ann. of Math. (2) 136 (1992), no. 3, 447-510. MR 93m:20065

[Gab97]

David Gabai, On the geometric and topological rigidity of hyperbolic -manifolds, J. Amer. Math. Soc. 10 (1997), no. 1, 37-74. MR 97h:57028

[GMT]

D. Gabai, R. Meyerhoff, and N. Thurston, Homotopy hyperbolic 3-manifolds are hyperbolic, Annals of Math, to appear.

[Gro87]

M. Gromov, Hyperbolic groups, Essays in group theory, Springer, New York, 1987, pp. 75-263. MR 89e:20070

[GS92]

Mikhail Gromov and Richard Schoen, Harmonic maps into singular spaces and -adic superrigidity for lattices in groups of rank one, Inst. Hautes Études Sci. Publ. Math. (1992), no. 76, 165-246. MR 94e:58032

[GW71]

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

[HK98]

Juha Heinonen and Pekka Koskela, Quasiconformal maps in metric spaces with controlled geometry, Acta Math. 181 (1998), no. 1, 1-61. MR 99j:30025

[Kap01]

Michael Kapovich, Hyperbolic manifolds and discrete groups, Birkhäuser Boston Inc., Boston, MA, 2001.

[KL97a]

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

[KL97b]

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

[KS93]

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

[Lee97]

B. Leeb, A characterization of irreducible symmetric spaces and euclidean buildings of higher rank by their asymptotic geometry, Preprint, June, 1997.

[LY72]

H. Blaine Lawson, Jr. and Shing Tung Yau, Compact manifolds of nonpositive curvature, J. Differential Geometry 7 (1972), 211-228. MR 48:12402

[McM96]

Curtis T. McMullen, Renormalization and 3-manifolds which fiber over the circle, Princeton University Press, Princeton, NJ, 1996. MR 97f:57022

[Min94]

Yair N. Minsky, On rigidity, limit sets, and end invariants of hyperbolic -manifolds, J. Amer. Math. Soc. 7 (1994), no. 3, 539-588. MR 94m:57029

[Min99]

Yair N. Minsky, The classification of punctured-torus groups, Ann. of Math. (2) 149 (1999), no. 2, 559-626. MR 2000f:30028

[Mos73]

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

[MS84]

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

[MSY93]

Ngaiming Mok, Yum Tong Siu, and Sai-Kee Yeung, Geometric superrigidity, Invent. Math. 113 (1993), no. 1, 57-83. MR 94h:53079

[Ota90]

Jean-Pierre Otal, Le spectre marqué des longueurs des surfaces à courbure négative, Ann. of Math. (2) 131 (1990), no. 1, 151-162.

[Ota96]

Jean-Pierre Otal, Le théorème d'hyperbolisation pour les variétés fibrées de dimension 3, Astérisque (1996), no. 235, x+159. MR 97e:57013

[Ota98]

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

[Pan89]

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

[RS94]

E. Rips and Z. Sela, Structure and rigidity in hyperbolic groups. I, Geom. Funct. Anal. 4 (1994), no. 3, 337-371. MR 96c:20067

[Sch95]

Richard Schwartz, The quasi-isometry classification of rank one lattices, Inst. Hautes Études Sci. Publ. Math. 82 (1995), 133-168. MR 97c:22014

[Sel95]

Z. Sela, The isomorphism problem for hyperbolic groups. I, Ann. of Math. (2) 141 (1995), no. 2, 217-283. MR 96b:20049