Add to ORKGThe aim of this paper is to provide two examples in Hilbert geometry which show that volume growth entropy is not always a limit on the one hand, and that it may vanish for a non-polygonal domain in the plane on the other hand
We study the asymptotic behaviour of the volume growth function of simply connected, Riemannian mani...
The volume entropy of a compact metric measure space is known to be the exponential growth rate of t...
20 pages. This note provides a detailed proof of a result announced in appendix A of a previous work...
International audienceWe show that the volume entropy of a Hilbert geometry on a convex body is exac...
International audienceWe show that the volume entropy of a Hilbert geometry on a convex body is exac...
We show that the volume entropy of a Hilbert geometry on a convex body is exactly twice the flag-app...
Abstract. The approximability of a convex body is a number which measures the difficulty to approxim...
Abstract. It is shown that the volume entropy of a Hilbert ge-ometry associated to an n-dimensional ...
Abstract. We prove that the metric balls of a Hilbert geometry admit a volume growth at least polyno...
International audienceIn this paper we provide two new characterizations of real hyperbolic $n$-spac...
International audienceWe prove that the Hilbert geometry of a product of convex sets is bi-lipschitz...
We prove a sharp inequality between the Blaschke and Hilbert distance on a proper convex domain: for...
International audienceWe prove, in the context of Hilbert geometry, the equivalence between the exis...
The moduli space of convex projective structures on a simplicial hyperbolic Coxeter orbifold is eith...
We study the asymptotic behaviour of the volume growth function of simply connected, Riemannian mani...
We study the asymptotic behaviour of the volume growth function of simply connected, Riemannian mani...
The volume entropy of a compact metric measure space is known to be the exponential growth rate of t...
20 pages. This note provides a detailed proof of a result announced in appendix A of a previous work...
International audienceWe show that the volume entropy of a Hilbert geometry on a convex body is exac...
International audienceWe show that the volume entropy of a Hilbert geometry on a convex body is exac...
We show that the volume entropy of a Hilbert geometry on a convex body is exactly twice the flag-app...
Abstract. The approximability of a convex body is a number which measures the difficulty to approxim...
Abstract. It is shown that the volume entropy of a Hilbert ge-ometry associated to an n-dimensional ...
Abstract. We prove that the metric balls of a Hilbert geometry admit a volume growth at least polyno...
International audienceIn this paper we provide two new characterizations of real hyperbolic $n$-spac...
International audienceWe prove that the Hilbert geometry of a product of convex sets is bi-lipschitz...
We prove a sharp inequality between the Blaschke and Hilbert distance on a proper convex domain: for...
International audienceWe prove, in the context of Hilbert geometry, the equivalence between the exis...
The moduli space of convex projective structures on a simplicial hyperbolic Coxeter orbifold is eith...
We study the asymptotic behaviour of the volume growth function of simply connected, Riemannian mani...
We study the asymptotic behaviour of the volume growth function of simply connected, Riemannian mani...
The volume entropy of a compact metric measure space is known to be the exponential growth rate of t...
20 pages. This note provides a detailed proof of a result announced in appendix A of a previous work...