Ballmann, W.; Buyalo, S. Nonpositively curved metrics on 2-polyhedra. (English) Zbl 0843.53036 Math. Z. 222, No. 1, 97-134 (1996). Summary: We consider metrics on compact 2-dimensional polyhedra which are nonpositively curved in the sense of Alexandrov. We are interested in the moduli space of such metrics and, in particular, in the question whether the metric is rigid. Cited in 1 ReviewCited in 3 Documents MSC: 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 57M20 Two-dimensional complexes (manifolds) (MSC2010) Keywords:compact 2-dimensional polyhedra; moduli space PDF BibTeX XML Cite \textit{W. Ballmann} and \textit{S. Buyalo}, Math. Z. 222, No. 1, 1 (1996; Zbl 0843.53036) Full Text: DOI EuDML OpenURL References: [1] Alexandrov, A.D.: Über eine Verallgemeinerung der Riemannschen Geometrie. Schriftenreihe des Forschungsinstituts für Mathematik; Berlin, Heft1, 33–84, (1957) [2] Alexandrov, A.D., Zalgaller, V.A.: Two dimensional manifolds of bounded curvature. Trudy Matem. Inst. Steklov63, (1962) [3] Ballmann, W.: Singular spaces of non-positive curvature. Chapitre 10 in: Ghys, E., de la Harpe, P., Sur les Groupes Hyperboliques d’après Mikhael Gromov. Birkhäuser, Boston, Basel, Berlin 1990 · Zbl 0731.20025 [4] Ballmann, W., Brin, M.: Polygonal complexes and combinatorial group theory. Geometriae Dedicata50, 165–191, (1994) · Zbl 0832.57002 [5] Benakli, N.: Polyèdre à géométrie locale donnée. C.R. Acad. Sci. Paris, t.313, SérieI, p. 561–564, 1991 · Zbl 0744.57003 [6] Borel, A., Harder, G.: Existence of discrete cocompact subgroups of reductive groups over local fields. J. reine Angew. Math.298, 53–64, (1978) · Zbl 0385.14014 [7] Brin, I.A.: The Gauss-Bonnet theorem for polyhedra. Uspeki. Mat. Nauk3, 226–227, (1948) [8] Brown, K.S.: Buildings. Springer 1989 [9] Cheeger, J., Gromov, M.:L 2-Cohomology and group cohomology. Topology25, 189–215 (1986) · Zbl 0597.57020 [10] Eberlein, P.: Geodesic flows in certain manifolds without conjugate points. Trans. Amer. Math. Soc.167, 151–170, (1972) · Zbl 0209.53304 [11] Gromov, M.: Hyperbolic groups. In: Essays in group theory, edited by M. Gersten. M.S.R.I. Publ.8, (Springer 1987), 75–263 [12] Gromov, M.: Asymptotic invariants of infinite groups. Geometric Group Theory, Vol. 2 (G.A. Noble & M.A. Roller, eds.). LMS Lecture Notes 182 (1993) · Zbl 0841.20039 [13] Gromov, M., Lafontaine, J., Pansu, P.: Structures mètriques pour les variétés riemanniennes. Cedic/Fernand Nathan, Paris 1981 [14] Haglund, F.: Les polyèdres de Gromov. C.R. Acad. Sci. Paris, t.313, Série I, p. 603–606, 1991 · Zbl 0749.52011 [15] Reshetnyak, Y.G.: Rotation of a curve in a manifold of bounded curvature with isothermic linear element. Siberian Math. J.4, 870–911, (1963) [16] Światkowski, J.: Polygonal complexes of nonpositive curvature: from local symmetry to global one. Preprint, Wroclaw 1993 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.