Affine functions on Alexandrov spaces
  We show that every finite-dimensional Alexandrov space X with curvature bounded from below embeds canonically into a product of an Alexandrov space with the same curvature bound and a Euclidean space such that each affine function on X comes from an affine function on the Euclidean space. 
Christian Lange and Stephan Stadler
math.MG math.DG