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In this work we study upper bounds for the ratio of successive inner andouter radii of a convex body K. This problem was studied by Perel'man andPukhov and it is a natural generalization of the classical results of Jung andSteinhagen. We also introduce a technique which relates sections andprojections of a convex body in an optimal way.

Improving bounds for the Perel'man-Pukhov quotient for inner and outer radii