Uniformly convex subsets of the Hilbert space with modulus of convexity   of the second order
  We prove that in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius. We also obtain an estimate of this radius. 
Maxim V. Balashov and Du\v{s}an Repov\v{s}
math.FA math.GN