43 citations · 139 across the 17 of their papers we have counts for
20 papers
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…
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…
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…
Finiteness Theorems for Gromov-Hyperbolic Spaces and Groups
Gérard Besson, Gilles Courtois, Sylvestre Gallot +1
In this article we prove that the set of torsion-free groups acting by isometries on a hyperbolic metric space whose entropy is bounded above and with a compact quotient is finite.…
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…
Curvature-Free Margulis Lemma for Gromov-Hyperbolic Spaces
Gérard Besson, Gilles Courtois, Sylvestre Gallot +1
We prove curvature-free versions of the celebrated Margulis Lemma. We are interested by both the algebraic aspects and the geometric ones, with however an emphasis on the second an…
Entropy and finiteness of groups with acylindrical splittings
Filippo Cerocchi, Andrea Sambusetti
We prove that there exists a positive, explicit function such that, for any group admitting a -acylindrical splitting and any generating set of with $\math…
Growth gap in hyperbolic groups and amenability
Rémi Coulon, Françoise Dal'Bo, Andrea Sambusetti
We prove a general version of the amenability conjecture in the unified setting of a Gromov hyperbolic group G acting properly cocompactly either on its Cayley graph, or on a CAT(-…
Local topological rigidity of non-geometric -manifolds
Filippo Cerocchi, Andrea Sambusetti
We study Riemannian metrics on compact, torsionless, non-geometric -manifolds, i.e. whose interior does not support any of the eight model geometries. We prove a lower bound "à…
Entropy Rigidity of negatively curved manifolds of finite volume
M. Peigne, A. Sambusetti
We prove the following entropy-rigidity result in finite volume: if is a negatively curved manifold with curvature , then if and only…
Asymptotic behavior of the Riemannian Heisenberg group and its horoboundary
Enrico Le Donne, Sebastiano Nicolussi Golo, Andrea Sambusetti
The paper is devoted to the large scale geometry of the Heisenberg group equipped with left-invariant Riemannian distances. We prove that two such distances have bounde…
Convergence and Counting in Infinite Measure
Françoise Dal'bo, Marc Peigné, Jean-Claude Picaud +1
We construct convergent and divergent lattices in negative curvature and give a precise asymptotic description of the behavior of their counting function.
Asymptotic geometry of negatively curved manifolds of finite volume
F. Dal'Bo, M. Peigné, J. C. Picaud +1
We study the asymptotic behaviour of simply connected, Riemannian manifolds of strictly negative curvature admitting a non-uniform lattice . If the quotient manifold $\bar X…
Quantitative Bounded Distance Theorem and Margulis' Lemma for Z^n actions with applications to homology
Filippo Cerocchi, Andrea Sambusetti
We consider the stable norm associated to a discrete, torsionless abelian group of isometries of a geodesic space . We show that the difference between…
On asymptotically harmonic manifolds of negative curvature
Philippe Castillon, Andrea Sambusetti
We study asymptotically harmonic manifolds of negative curvature, without any cocompactness or homogeneity assumption. We show that asymptotic harmonicity provides a lot of informa…
On the horoboundary and the geometry of rays of negatively curved manifolds
Françoise Dal'bo, Marc Peigné, Andréa Sambusetti
In this paper we try to compare the "horoboundary" of a (not necessarily simply connected) negatively curved complete Riemannian manifold X with the visual one and describe with ex…
Submanifolds, Isoperimetric Inequalities and Optimal Transportation
Philippe Castillon
The aim of this paper is to prove isoperimetric inequalities on submanifolds of the Euclidean space using mass transportation methods. We obtain a sharp ?weighted isoperimetric ine…
On the growth of nonuniform lattices in pinched negatively curved manifolds
Françoise Dal'Bo, Marc Peigné, Jean-Claude Picaud +1
We study the relation between the exponential growth rate of volume in a pinched negatively curved manifold and the critical exponent of its lattices. These objects have a long and…