Let $ X $ be a complete simply connected riemannian manifold of pinched negative curvature, and let $ X_C $ be the compactification obtained by adjoining the ideal sphere. We show that the closed convex hull of a closed subset of $ X_C $ varies continuously with respect to the Hausdorff topology. We show that the volume of the set of $ n $ points in $ X_C $ is finite, and bounded in terms of $ n $, the dimension of $ X_C $, and the pinching constants of $ X_C $. We also show that this volume varies continuously as a function of these $ n $ points, provided that no two are ever equal to the same ideal point.
Comment. Math. Helv. 69 (1994) 49-81.