Local characterization of strongly convex sets
  Strongly convex sets in Hilbert spaces are characterized by local properties. One quantity which is used for this purpose is a generalization of the modulus of convexity \delta_\Omega of a set \Omega. We also show that \lim_{\epsilon \to 0} \delta_\Omega(\epsilon)/\epsilon^2 exists whenever \Omega is closed and convex. 
Alexander Weber, Gunther Rei{\ss}ig
math.MG math.FA math.OC