Orbihedra of nonpositive curvature

Werner Ballmann; Michael Brin

Publications Mathématiques de l'IHÉS (1995)

  • Volume: 82, page 169-209
  • ISSN: 0073-8301

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Ballmann, Werner, and Brin, Michael. "Orbihedra of nonpositive curvature." Publications Mathématiques de l'IHÉS 82 (1995): 169-209. <http://eudml.org/doc/104108>.

@article{Ballmann1995,
author = {Ballmann, Werner, Brin, Michael},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {rank; rigidity for rank at least 2; orbihedron; nonpositive curvature; Euclidean building},
language = {eng},
pages = {169-209},
publisher = {Institut des Hautes Études Scientifiques},
title = {Orbihedra of nonpositive curvature},
url = {http://eudml.org/doc/104108},
volume = {82},
year = {1995},
}

TY - JOUR
AU - Ballmann, Werner
AU - Brin, Michael
TI - Orbihedra of nonpositive curvature
JO - Publications Mathématiques de l'IHÉS
PY - 1995
PB - Institut des Hautes Études Scientifiques
VL - 82
SP - 169
EP - 209
LA - eng
KW - rank; rigidity for rank at least 2; orbihedron; nonpositive curvature; Euclidean building
UR - http://eudml.org/doc/104108
ER -

References

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  1. [AlBi] S. B. ALEXANDER and R. L. BISHOP, The Hadamard-Cartan theorem in locally convex metric spaces, L'Enseignement math., 36 (1990), 309-320. Zbl0718.53055MR92c:53044
  2. [Ale] A. D. ALEXANDROV, A theorem on triangles in a metric space and some applications, Trudy Math. Inst. Steklov, 38 (1951), 5-23 (Russian). MR14,198a
  3. [Ba1] W. BALLMANN, Axial isometries of manifolds of nonpositive curvature, Math. Ann., 259 (1982), 131-144. Zbl0487.53039MR83i:53068
  4. [Ba2] W. BALLMANN, Lectures on Spaces of Nonpositive Curvature, Birkhäuser Verlag, 1995. Zbl0834.53003MR97a:53053
  5. [Ba3] W. BALLMANN, Nonpositively curved manifolds of higher rank, Annals of Math., 122 (1985), 597-609. Zbl0585.53031MR87e:53059
  6. [BaBr] W. BALLMANN and M. BRIN, Polygonal complexes and combinatorial group theory, Geometriae Dedicata, 50 (1994), 165-191. Zbl0832.57002MR95e:57004
  7. [BBE] W. BALLMANN, M. BRIN and P. EBERLEIN, Structure of manifolds of nonpositive curvature, I, Annals of Math., 122 (1985), 171-203. Zbl0589.53047MR87c:58092a
  8. [BBS] W. BALLMANN, M. BRIN and R. SPATZIER, Structure of manifolds of nonpositive curvature, II, Annals of Math., 122 (1985), 205-235. Zbl0598.53046MR87c:58092b
  9. [BaBu] W. BALLMANN and S. BUYALO, Nonpositively curved metrics on 2-polyhedra, Math. Zeitschrift (to appear). Zbl0843.53036
  10. [Bro] K. S. BROWN, Buildings, Springer-Verlag, 1988. Zbl0715.20017
  11. [BrTi] F. BRUHAT and J. TITS, Groupes réductifs sur un corps local, I, Données radicielles valuées, Publications Math. IHES, 40 (1972), 5-251. Zbl0254.14017MR48 #6265
  12. [BuSp] K. BURNS and R. SPATZIER, Manifolds of nonpositive curvature and their buildings, Publications Math. IHES, 65 (1987), 35-59. Zbl0643.53037MR88g:53050
  13. [Bus] H. BUSEMANN, Spaces with nonpositive curvature, Acta Mathematica, 80 (1948), 259-310. Zbl0038.10005MR10,623g
  14. [ChEb] S.-S. CHEN and P. EBERLEIN, Isometry groups of simply connected manifolds of nonpositive curvature, Ill. J. Math., 24 (1980), 73-103. Zbl0413.53029MR82k:53052
  15. [CFS] I. P. CORNFELD, S. V. FOMIN and Ya. G. SINAI, Ergodic Theory, Springer-Verlag, 1982. Zbl0493.28007
  16. [Eb1] P. EBERLEIN, Lattices in spaces of nonpositive curvature, Annals of Math., 111 (1980), 435-476. Zbl0401.53015MR82m:53040
  17. [Eb2] P. EBERLEIN, Geodesic rigidity in compact nonpositively curved manifolds, Trans. Amer. Math. Soc., 268 (1981), 411-443. Zbl0526.53045MR83a:53039
  18. [EbHe] P. EBERLEIN and J. HEBER, A differential geometric characterization of symmetric spaces of higher rank, Publications Math. IHES, 71 (1990), 33-44. Zbl0722.53041MR91j:53022
  19. [Gr1] M. GROMOV, Hyperbolic groups, Essays in Group Theory (S. M. GERSTEN, ed.), MSRI Publ. 8, Springer-Verlag, 1987, 75-264. Zbl0634.20015MR89e:20070
  20. [Gr2] M. GROMOV, Structures métriques pour les variétés riemanniennes, rédigé par J. Lafontaine et P. Pansu, Cedic/Fernand Nathan, 1981. Zbl0509.53034MR85e:53051
  21. [Kle] B. KLEINER, A metric characterization of Tits buildings, in preparation (1995). 
  22. [Kni] G. KNIEPER, Das Wachstum der Äquivalenzklassen geschlossener Geodätischen in kompakten Mannigfaltigkeiten, Archiv. Math., 40 (1983), 559-568. Zbl0504.53041MR85h:58139
  23. [LySc] R. LYNDON and P. SCHUPP, Combinatorial Group Theory, Springer-Verlag, 1977. Zbl0368.20023MR58 #28182
  24. [Mor] M. MORSE, A fundamental class of geodesics on any surface of genus greater than one, Trans. Amer. Math. Soc., 26 (1924), 25-60. Zbl50.0466.04MR1501263JFM50.0466.04
  25. [Ti1] J. TITS, Free subgroups in linear groups, J. Algebra, 20 (1972), 250-270. Zbl0236.20032MR44 #4105
  26. [Ti2] J. TITS, Buildings of spherical type and finite BN-pairs, Lecture Notes in Math., 386, Springer-Verlag, 1974. Zbl0295.20047MR57 #9866
  27. [Wa1] A. WALD, Begründung einer koordinatenlosen Differentialgeometrie der Flächen, Ergebnisse math. Kolloquium Wien, 7 (1935), 24-46. Zbl0014.23001JFM62.0806.01

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