Orbihedra of nonpositive curvature
Publications Mathématiques de l'IHÉS, Tome 82 (1995), pp. 169-209 
@article{PMIHES_1995__82__169_0,
     author = {Ballmann, Werner and Brin, Michael},
     title = {Orbihedra of nonpositive curvature},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {169--209},
     year = {1995},
     publisher = {Institut des Hautes Etudes Scientifiques},
     volume = {82},
     mrnumber = {97i:53049},
     zbl = {0866.53029},
     language = {en},
     url = {https://www.numdam.org/item/PMIHES_1995__82__169_0/}
}
TY  - JOUR
AU  - Ballmann, Werner
AU  - Brin, Michael
TI  - Orbihedra of nonpositive curvature
JO  - Publications Mathématiques de l'IHÉS
PY  - 1995
SP  - 169
EP  - 209
VL  - 82
PB  - Institut des Hautes Etudes Scientifiques
UR  - https://www.numdam.org/item/PMIHES_1995__82__169_0/
LA  - en
ID  - PMIHES_1995__82__169_0
ER  - 
%0 Journal Article
%A Ballmann, Werner
%A Brin, Michael
%T Orbihedra of nonpositive curvature
%J Publications Mathématiques de l'IHÉS
%D 1995
%P 169-209
%V 82
%I Institut des Hautes Etudes Scientifiques
%U https://www.numdam.org/item/PMIHES_1995__82__169_0/
%G en
%F PMIHES_1995__82__169_0
Ballmann, Werner; Brin, Michael. Orbihedra of nonpositive curvature. Publications Mathématiques de l'IHÉS, Tome 82 (1995), pp. 169-209. https://www.numdam.org/item/PMIHES_1995__82__169_0/

[AlBi] S. B. Alexander and R. L. Bishop, The Hadamard-Cartan theorem in locally convex metric spaces, L'Enseignement math., 36 (1990), 309-320. | Zbl | MR

[Ale] A. D. Alexandrov, A theorem on triangles in a metric space and some applications, Trudy Math. Inst. Steklov, 38 (1951), 5-23 (Russian). | MR

[Ba1] W. Ballmann, Axial isometries of manifolds of nonpositive curvature, Math. Ann., 259 (1982), 131-144. | Zbl | MR

[Ba2] W. Ballmann, Lectures on Spaces of Nonpositive Curvature, Birkhäuser Verlag, 1995. | Zbl | MR

[Ba3] W. Ballmann, Nonpositively curved manifolds of higher rank, Annals of Math., 122 (1985), 597-609. | Zbl | MR

[BaBr] W. Ballmann and M. Brin, Polygonal complexes and combinatorial group theory, Geometriae Dedicata, 50 (1994), 165-191. | Zbl | MR

[BBE] W. Ballmann, M. Brin and P. Eberlein, Structure of manifolds of nonpositive curvature, I, Annals of Math., 122 (1985), 171-203. | Zbl | MR

[BBS] W. Ballmann, M. Brin and R. Spatzier, Structure of manifolds of nonpositive curvature, II, Annals of Math., 122 (1985), 205-235. | Zbl | MR

[BaBu] W. Ballmann and S. Buyalo, Nonpositively curved metrics on 2-polyhedra, Math. Zeitschrift (to appear). | Zbl

[Bro] K. S. Brown, Buildings, Springer-Verlag, 1988. | Zbl

[BrTi] F. Bruhat and J. Tits, Groupes réductifs sur un corps local, I, Données radicielles valuées, Publications Math. IHES, 40 (1972), 5-251. | Zbl | MR | Numdam

[BuSp] K. Burns and R. Spatzier, Manifolds of nonpositive curvature and their buildings, Publications Math. IHES, 65 (1987), 35-59. | Zbl | MR | Numdam

[Bus] H. Busemann, Spaces with nonpositive curvature, Acta Mathematica, 80 (1948), 259-310. | Zbl | MR

[ChEb] S.-S. Chen and P. Eberlein, Isometry groups of simply connected manifolds of nonpositive curvature, Ill. J. Math., 24 (1980), 73-103. | Zbl | MR

[CFS] I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer-Verlag, 1982. | Zbl | MR

[Eb1] P. Eberlein, Lattices in spaces of nonpositive curvature, Annals of Math., 111 (1980), 435-476. | Zbl | MR

[Eb2] P. Eberlein, Geodesic rigidity in compact nonpositively curved manifolds, Trans. Amer. Math. Soc., 268 (1981), 411-443. | Zbl | MR

[EbHe] P. Eberlein and J. Heber, A differential geometric characterization of symmetric spaces of higher rank, Publications Math. IHES, 71 (1990), 33-44. | Zbl | Numdam | MR | EuDML

[Gr1] M. Gromov, Hyperbolic groups, Essays in Group Theory (S. M. GERSTEN, ed.), MSRI Publ. 8, Springer-Verlag, 1987, 75-264. | Zbl | MR

[Gr2] M. Gromov, Structures métriques pour les variétés riemanniennes, rédigé par J. Lafontaine et P. Pansu, Cedic/Fernand Nathan, 1981. | Zbl | MR

[Kle] B. Kleiner, A metric characterization of Tits buildings, in preparation (1995).

[Kni] G. Knieper, Das Wachstum der Äquivalenzklassen geschlossener Geodätischen in kompakten Mannigfaltigkeiten, Archiv. Math., 40 (1983), 559-568. | Zbl | MR

[LySc] R. Lyndon and P. Schupp, Combinatorial Group Theory, Springer-Verlag, 1977. | Zbl | MR

[Mor] M. Morse, A fundamental class of geodesics on any surface of genus greater than one, Trans. Amer. Math. Soc., 26 (1924), 25-60. | MR | JFM

[Ti1] J. Tits, Free subgroups in linear groups, J. Algebra, 20 (1972), 250-270. | Zbl | MR

[Ti2] J. Tits, Buildings of spherical type and finite BN-pairs, Lecture Notes in Math., 386, Springer-Verlag, 1974. | Zbl | MR

[Wa1] A. Wald, Begründung einer koordinatenlosen Differentialgeometrie der Flächen, Ergebnisse math. Kolloquium Wien, 7 (1935), 24-46. | Zbl | JFM