Results 1 to 10 of about 1,086,676 (318)
Parabolic isometries of CAT(0) spaces and CAT(0) dimensions [PDF]
Algebr. Geom. Topol. 4 (2004) 861-892, 2003 We study discrete groups from the view point of a dimension gap in connection to CAT(0) geometry. Developing studies by Brady-Crisp and Bridson, we show that there exist finitely presented groups of geometric dimension 2 which do not act properly on any ...
Ballmann +15 more
core +12 more sources
Mann iteration for monotone nonexpansive mappings in ordered CAT(0) space with an application to integral equations [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we establish some convergence results for a monotone nonexpansive mapping in a CAT(0) $\operatorname{CAT}(0)$ space. We prove the Δ- and strong convergence of the Mann iteration scheme. Further, we provide a numerical example to illustrate
Izhar Uddin +2 more
doaj +2 more sources
Contracting Boundaries of CAT(0) Spaces [PDF]
Journal of Topology, 2013 As demonstrated by Croke and Kleiner, the visual boundary of a CAT(0) group is not well-defined since quasi-isometric CAT(0) spaces can have non-homeomorphic boundaries.
Charney, Ruth, Sultan, Harold
core +5 more sources
Collapsibility of CAT(0) spaces [PDF]
Geometriae Dedicata, 2019 27 pages, 3 figures. The part on collapsibility of convex complexes has been removed and forms a new paper, called "Barycentric subdivisions of convexes complex are collapsible" (arXiv:1709.07930). The part on enumeration of manifolds has also been removed and forms now a third paper, called "A Cheeger-type exponential bound for the number of ...
Karim Adiprasito, Bruno Benedetti
openaire +7 more sources
CAT(0) spaces of higher rank II [PDF]
Inventiones mathematicae, 2023 AbstractThis belongs to a series of papers motivated by Ballmann’s Higher Rank Rigidity Conjecture. We prove the following. Let $X$ X be a CAT(0) space with a geometric group action $\Gamma \curvearrowright X$ Γ ↷ X . Suppose that every geodesic in $
Stephan Stadler
+9 more sources
CAT(0) spaces on which a certain type of singularity is bounded [PDF]
, 2010 In this paper, we present a geometric condition for a family of CAT(0) spaces, which ensures that the Izeki-Nayatani invariants of spaces in the family are uniformly bounded from above by a constant strictly less than 1.
Toyoda, Tetsu
core +2 more sources
On splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature [PDF]
arXiv, 2004 In this paper, we show some splitting theorems for CAT(0) spaces on which a product group acts geometrically and we obtain a splitting theorem for compact geodesic spaces of non-positive curvature. A CAT(0) group $\Gamma$ is said to be {\it rigid}, if $\Gamma$ determines the boundary up to homeomorphisms of a CAT(0) space on which $\Gamma$ acts ...
Tetsuya Hosaka
arxiv +3 more sources
Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces [PDF]
Journal of Applied Mathematics, 2012 Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces are studied. Consider a nonexpansive self-mapping T of a closed convex subset C of a CAT(0) space X. Suppose that the set Fix(T) of fixed points of T is nonempty.
Luo Yi Shi, Ru Dong Chen
doaj +2 more sources
Geodesic flow for CAT(0)-groups [PDF]
Geom. Topol. 16 (2012) 1345-1391, 2010 We associate to a CAT(0)-space a flow space that can be used as the replacement for the geodesic flow on the sphere tangent bundle of a Riemannian manifold.
Arthur Bartels +7 more
core +3 more sources
Parabolic subgroups of Coxeter groups acting by reflections on CAT(0) spaces [PDF]
arXiv, 2004 We consider a cocompact discrete reflection group $W$ of a CAT(0) space $X$. Then $W$ becomes a Coxeter group. In this paper, we study an analogy between the Davis-Moussong complex $\Sigma(W,S)$ and the CAT(0) space $X$, and show several analogous results about the limit set of a parabolic subgroup of the Coxeter group $W$.
Tetsuya Hosaka
arxiv +3 more sources