![]() Delzant, Thomas Sous-groupes distingués et quotients des groupes hyperboliques, Duke Math. Sets of matrices all infinite products of which converge, Linear Algebra Appl. de Cornulier, Yves Tessera, Romain Valette, Alain Isometric group actions on Hilbert spaces: growth of cocycles, Geom. Les groupes hyperboliques de Gromov, Lecture Notes in Mathematics, 1441, Springer, 1990, x 165 pages Coornaert, Michel Delzant, Thomas Papadopoulos, Athanase Géométrie et théorie des groupes. Chiswell, Ian Introduction to Λ-trees, World Scientific, 2001, xii 315 pages Estellon, Bertrand Habib, Michel Vaxès, Yann Diameters, centers, and approximating trees of δ-hyperbolic geodesic spaces and graphs, Computational geometry (SCG’08), ACM Press, 2008, pp. Géom.), Volume 18, Université de Grenoble I, 2000, pp. Champetier, Christophe Guirardel, Vincent Monoïdes libres dans les groupes hyperboliques, Séminaire de Théorie Spectrale et Géométrie, Vol. Caprace, Pierre-Emmanuel Lytchak, Alexander At infinity of finite-dimensional CAT(0) spaces, Math. Burger, Marc Pozzetti, Maria Beatrice Maximal representations, non-Archimedean Siegel spaces, and buildings, Geom. Geometric inequalities, Grundlehren der Mathematischen Wissenschaften, 285, Springer, 1988, xiv 331 pages (Translated from the Russian by A. Haefliger, André Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften, 319, Springer, 1999, xxii 643 pages Breuillard, Emmanuel Green, Ben Tao, Terence The structure of approximate groups, Publ. Breuillard, Emmanuel Green, Ben Guralnick, Robert Tao, Terence Strongly dense free subgroups of semisimple algebraic groups, Isr. Breuillard, Emmanuel Gelander, Tsachik Uniform independence in linear groups, Invent. Breuillard, Emmanuel A height gap theorem for finite subsets of GL d ( ℚ ¯ ) and nonamenable subgroups, Ann. ![]() Breuillard, Emmanuel A strong Tits alternative (2008) ( ) Breuillard, Emmanuel Effective estimates for the spectral radius of a bounded set of matrices (unpublished note available upon request) A course on geometric group theory, MSJ Memoirs, 16, Mathematical Society of Japan, 2006, x 104 pages On free subgroups of semisimple groups, Enseign. , 36, Springer, 1998, x 430 pages (Translated from the 1987 French original, Revised by the authors) Bochnak, Jacek Coste, Michel Roy, Marie-Françoise Real algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete. Bochi, Jairo Inequalities for numerical invariants of sets of matrices, Linear Algebra Appl. Bestvina, Mladen ℝ-trees in topology, geometry, and group theory, Handbook of geometric topology, North-Holland, 2002, pp. Besson, Gérard Courtois, Gilles Gallot, Sylvestre Sambusetti, Andrea Curvature-Free Margulis Lemma for Gromov-Hyperbolic Spaces (2017) ( ) Besson, Gérard Courtois, Gilles Gallot, Sylvestre Uniform growth of groups acting on Cartan-Hadamard spaces, J. Wang, Yang Bounded semigroups of matrices, Linear Algebra Appl. Bass, Hyman Groups of integral representation type, Pac. Bartholdi, Laurent de Cornulier, Yves Infinite groups with large balls of torsion elements and small entropy, Arch. A lower bound on the growth of word hyperbolic groups, J. Lustig, Martin Reeves, Laurence Short, Hamish Ventura, Enric Uniform non-amenability, Adv. Schmitz.Abels, Herbert Margulis, Gregory Coarsely geodesic metrics on reductive groups, Modern dynamical systems and applications, Cambridge University Press, 2004, pp. The total absolute curvature of closed curves in Riemannian manifolds. ![]() I would really prefer something metric independent if possible. However, this would depend strongly on the metrics/contraction maps involved. It seems that one could derive some inequality from the usual one using contraction maps to and from Euclidean space and estimating the resulting effect on the total curvature along $\gamma$. Is there a version of the Fáry-Milnor theorem for positively curved metrics on $S^3$? ![]() I'm interested in the opposite situation. the usual hyperbolic metric), maybe satisfying some extra hypotheses (for example, see ). (Fáry-Milnor) If a simple closed curve $\gamma \subset \mathbb^3$ is equipped with a non-positively curved metric (e.g. I'm interested in generalizations the following well-known theorem of Fáry and Milnor. ![]()
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