Abstract We present a generalization of the notion neighborliness to non-polyhedral convex cones. Although definition is available in case literature, it fairly restrictive as requires all low-dimensional faces be polyhedral. Our approach more flexible and includes, for example, cone positive-semidefinite matrices special (this not neighborly general). term our Terracini convexity due its conce...

Ricci curvature bounds in Riemannian geometry are known to be equivalent to the weak convexity (convexity along at least one geodesic between any two points) of certain functionals in the space of probability measures. We prove that the weak convexity can be reinforced into strong (usual) convexity, thus solving a question left open in [4].

We use the theory of abstract convexity to study adverse-selection principal-agent problems and two-sided matching problems, departing from much of the literature by not requiring quasilinear utility. We formulate and characterize a basic underlying implementation duality. We show how this duality can be used to obtain a sharpening of the taxation principle, to obtain a general existence result...