Asymptotic topological regularity of CAT(0) spaces

Abstract

We study asymptotic topological regularity of CAT(0) spaces. We prove that if a purely n-dimensional, proper, geodesically complete CAT(0) space has small volume growth, then it is homeomorphic to the n-dimensional Euclidean space. We also discuss asymptotic geometry of proper, geodesically complete CAT(0) spaces of small volume growth.

35 pages

References in corpus (2)

• A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry
• Extending a rigidity result of Lytchak

Cited by in corpus (1)

• CAT(0) 4-manifolds are Euclidean