Quasiflats in CAT(0) complexes
  We show that if X is a piecewise Euclidean 2-complex with a cocompact isometry group, then every 2-quasiflat in X is at finite Hausdorff distance from a subset which is locally flat outside a compact set, and asymptotically conical. 
Mladen Bestvina, Bruce Kleiner, Michah Sageev