A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry
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Publication:2726208
zbMath1005.53031arXiv0903.0584MaRDI QIDQ2726208
Publication date: 15 July 2001
Full work available at URL: https://arxiv.org/abs/0903.0584
Global Riemannian geometry, including pinching (53C20) Rigidity results (53C24) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Differential geometry of symmetric spaces (53C35)
Related Items (40)
Rigidity at infinity of trees and Euclidean buildings ⋮ The Tits boundary of a $\text {CAT}(0)$ 2-complex ⋮ Metric Properties of Euclidean Buildings ⋮ Opposition diagrams for automorphisms of large spherical buildings ⋮ Affine maps between CAT(0) spaces ⋮ Tits Alternative for -dimensional complexes ⋮ Groups acting on CAT(0) square complexes ⋮ Curve Complexes Versus Tits Buildings: Structures and Applications ⋮ Hadamard spaces with isolated flats. (With an appendix written jointly with Mohamad Hindawi). ⋮ Fixed points and amenability in non-positive curvature ⋮ Polygons in buildings and their refined side lengths ⋮ Dynamics on flag manifolds: domains of proper discontinuity and cocompactness ⋮ Domesticity in generalized quadrangles ⋮ Morse quasiflats. II ⋮ On triples of ideal chambers in \(A_2\)-buildings ⋮ Opposition diagrams for automorphisms of small spherical buildings ⋮ Relativizing characterizations of Anosov subgroups. I (with an appendix by Gregory A. Soifer) ⋮ The combinatorics of automorphisms and opposition in generalised polygons ⋮ Infinite dimensional representations of orthogonal groups of quadratic forms with finite index ⋮ An obstruction to the smoothability of singular nonpositively curved metrics on 4-manifolds by patterns of incompressible tori ⋮ Anosov subgroups: dynamical and geometric characterizations ⋮ An indiscrete Bieberbach theorem: from amenable \(\mathrm{CAT}(0)\) groups to Tits buildings ⋮ Collineations of polar spaces with restricted displacements ⋮ \(\mathrm{CAT}(0)\) spaces of higher rank. I ⋮ CAT(0) spaces of higher rank. II ⋮ Connected components of the compactification of representation spaces of surface groups ⋮ Combinatorial and group-theoretic compactifications of buildings ⋮ Tits alternative for closed real analytic 4-manifolds of nonpositive curvature. ⋮ Coarse equivalences of Euclidean buildings. (With an appendix by Jeroen Schillewaert and Koen Struyve.) ⋮ Quasi-isometric embeddings of symmetric spaces and lattices: reducible case ⋮ Convex rank 1 subsets of Euclidean buildings (of type \(A_{2}\)) ⋮ Induced quasi-actions: A remark ⋮ Superrigidity of actions on finite rank median spaces ⋮ Isometry groups of non-positively curved spaces: structure theory ⋮ A ‘transversal’ for minimal invariant sets in the boundary of a CAT(0) group ⋮ Piecewise Euclidean structures and Eberlein's rigidity theorem in the singular case ⋮ A rank rigidity result for CAT(0) spaces with one-dimensional Tits boundaries ⋮ Invariant weakly convex cocompact subspaces for surface groups in $A_2$-buildings ⋮ Gelfand pairs and strong transitivity for Euclidean buildings ⋮ Asymptotic topological regularity of \(\mathrm{CAT}(0)\) spaces
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