Asymptotic dimension of a hyperbolic space and capacity dimension of its boundary at infinity

摘要

A quasisymmetry invariant of a metric space (called the capacity dimension, cdim Z) is introduced. The main result says that the asymptotic dimension of a visual Gromov hyperbolic space X is at most the capacity dimension of its boundary at infinity plus 1, asdim X≤cdim ∞X+1.