7 citations · 7 across the 14 of their papers we have counts for
11 papers · 1 filter
CAT(0) spaces quasi-isometric to Euclidean spaces
Nicola Cavallucci, Andrea Sambusetti
We show that if a proper, geodesically complete, CAT(0) homology manifold is quasi-isometric to the Euclidean space R^n then it is homeomorphic to R^n. On the other hand, we show t…
Otal-Peigné's Theorem for Gromov-hyperbolic spaces
Nicola Cavallucci
We extend the classical Otal-Peigné's Theorem to the class of proper, Gromov-hyperbolic spaces that are line-convex. Namely, we prove that when a group acts discretely and virtuall…
Convergence and collapsing of CAT-lattices
Nicola Cavallucci, Andrea Sambusetti
We study the theory of convergence for CAT-lattices (that is groups acting geometrically on proper, geodesically complete CAT-spaces) and their quotients (CAT-or…
GH-convergence of CAT-spaces: stability of the Euclidean factor
Nicola Cavallucci
We prove that if a sequence of geodesically complete CAT-spaces with uniformly cocompact discrete groups of isometries converges in the Gromov-Hausdorff sense to $X_\inf…
A GH-compactification of CAT-groups via totally disconnected, unimodular actions
Nicola Cavallucci
We give a detailed description of the possible limits in the equivariant-Gromov-Hausdorff sense of sequences , where the 's are proper, geodesically complete, unifo…
Thin actions on CAT(0) spaces
Nicola Cavallucci, Andrea Sambusetti
We study groups of isometries of packed, geodesically complete, CAT-spaces for which the systole at every point is smaller than a universal constant depending only on the pack…
The -completion of the space of Riemannian metrics is CAT: a shorter proof
Nicola Cavallucci
We reprove in an easier way a result of Brian Clarke: the completion of the space of Riemannian metrics of a compact, orientable smooth manifold with respect to the -distance…
Ahlfors regular conformal dimension and Gromov-Hausdorff convergence
Nicola Cavallucci
We prove that the Ahlfors regular conformal dimension is upper semicontinuous with respect to Gromov-Hausdorff convergence when restricted to the class of uniformly perfect, unifor…
Continuity of critical exponent of quasiconvex-cocompact groups under Gromov-Hausdorff convergence
Nicola Cavallucci
We show continuity under equivariant Gromov-Hausdorff convergence of the critical exponent of discrete, non-elementary, torsion-free, quasiconvex-cocompact groups with uniformly bo…
Discrete groups of packed, non-positively curved, Gromov hyperbolic metric spaces
Nicola Cavallucci, Andrea Sambusetti
We prove a quantitative version of the classical Tits' alternative for discrete groups acting on packed Gromov-hyperbolic spaces supporting a convex geodesic bicombing. Some geomet…
Packing and doubling in metric spaces with curvature bounded above
Nicola Cavallucci, Andrea Sambusetti
We study locally compact, locally geodesically complete, locally CAT(k) spaces (GCBA(k)-spaces). We prove a Croke-type local volume estimate only depending on the dimension of thes…