10 citations · 16 across the 5 of their papers we have counts for
6 papers · 1 filter
Dimension of locally and asymptotically self-similar spaces
Sergei Buyalo, Nina Lebedeva
We obtain two in a sense dual to each other results: First, that the capacity dimension of every compact, locally self-similar metric space coincides with the topological dimension…
Capacity dimension and embedding of hyperbolic spaces into the product of trees
S. Buyalo
We prove that every visual Gromov hyperbolic space X whose boundary at infinity has the finite capacity dimension n admits a quasi-isometric embedding into (n+1)-fold product of me…
Asymptotic dimension of a hyperbolic space and capacity dimension of its boundary at infinity
S. Buyalo
We introduce a quasi-symmetry invariant of a metric space Z called the capacity dimension. Our main result says that for a visual Gromov hyperbolic space X the asymptotic dimension…
Hyperbolic dimension of metric spaces
S. Buyalo, V. Schroeder
We introduce a new quasi-isometry invariant of metric spaces called the hyperbolic dimension, hypdim, which is a version of the Gromov's asymptotic dimension, asdim. The hyperbolic…
Embedding of hyperbolic spaces in the product of trees
S. Buyalo, V. Schroeder
We show that for each n\ge 2 there is a quasi-isometric embedding of the hyperbolic space H^n in the product T^n=Tx...xT of n copies of a (simplicial) metric tree T. On the other h…
Topological and geometric properties of graph-manifolds
S. Buyalo, P. Svetlov
This is an exposition of results on the existence problem of -injective immersed and embedded surfaces in graph-manifolds, and also of nonpositively curved metrics on graph-ma…