On the capacity dimension of the boundary of CAT(0) spaces

2019/04/02 by Wang, Dawei
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1904.01609

Abstract

In this paper, we study the capacity dimension of the boundary of CAT(0) spaces. We first compare the two metrics on the boundary of a hyperbolic CAT(0) space, i.e., the visual metric and the conical metric, and prove that they give the same capacity dimension of the boundary. Then we study the capacity dimension of the boundary of buildings, which is an important class of CAT(0) spaces. Finally, we give a possible method to prove the finiteness of the asymptotic dimension of CAT(0) spaces.

Related

• Metrics on Visual Boundaries of CAT(0) Spaces
• Asymptotic topological regularity of CAT(0) spaces
• Asymptotic dimension of proper CAT(0) spaces which are homeomorphic to the plane
• The Boundary at Infinity of a rough CAT(0) space
• Asymptotic Dimension and Boundaries of Hyperbolic Spaces