7 citations · 7 across the 14 of their papers we have counts for
15 papers
The entropy of Gromov-Thurston manifolds and branched coverings
Nicola Cavallucci, Merlin Incerti-Medici
We develop a general theory for the dynamics of the geodesic flow of locally CAT(k) branched coverings and we show that it does not depend on the specific covering but only on the…
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 $X_\inf…
A GH-compactification of CAT-groups via totally disconnected, unimodular actions
Nicola Cavallucci
We give a detailed description of the possible limits in the equivariant-Gromov-Hausdorff sense of sequences , where the 's are proper, geodesically complete, unifo…
Finiteness of CAT(0) group actions
Nicola Cavallucci, Andrea Sambusetti
We prove some finiteness results for discrete isometry groups of uniformly packed CAT-spaces with uniformly bounded codiameter (up to group isomorphism), and for CAT$(…
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…
Bishop-Jones' Theorem and the ergodic limit set
Nicola Cavallucci
For a proper, Gromov-hyperbolic metric space and a discrete, non-elementary, group of isometries, we define a natural subset of the limit set at infinity of the group called the er…
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…
Entropies of non positively curved metric spaces
Nicola Cavallucci
We show the equivalences of several notions of entropy, like a version of the topological entropy of the geodesic flow and the Minkowski dimension of the boundary, in metric spaces…
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…