The metric completion of a locally CAT(0) space

Daniel Allcock, Austin and IAS

If X is an noncomplete nonpositively curved space (formally: it is locally
CAT(0)) then its completion may easily fail to be.  But in some interesting
cases the completion is CAT(0), for example Teichmuller space and the many
branched covers of Riemannian manifolds over totally geodesic submanifolds.
We have found a simple criterion which forces X to be CAT(0). Its key
hypothesis is a statement about X *near* the boundary but not at the
boundary.