Improving bounds for the Perel'man-Pukhov quotient for inner and outer   radii
  In this work we study upper bounds for the ratio of successive inner and outer radii of a convex body K. This problem was studied by Perel'man and Pukhov and it is a natural generalization of the classical results of Jung and Steinhagen. We also introduce a technique which relates sections and projections of a convex body in an optimal way. 
Bernardo Gonz\'alez Merino
math.MG