  We provide sufficient conditions as to when a boundary component of a
cocompact convex set in a CAT(0)-space is contractible. We then use this to
study when the limit set of a quasi-convex, codimension one subgroup of a
negatively curved manifold group is `wild' in the boundary. The proof is based
on a notion of coarse upper curvature bounds in terms of barycenters and the
careful study of interpolation in geodesic metric spaces.
