Geodesic
Improving Bounds for the Perel'man-Pukhov Quotient for Inner and Outer Radii
Journal of convex analysis, Tome 24 (2017) no. 4, pp. 1099-1116
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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.
Classification : 52A20, 52A40
Mots-clés : Inner and outer radii, Perel'man-Pukhov inequality, Section and projection, Jung's inequality, Steinhagen's inequality 
@article{JCA_2017_24_4_JCA_2017_24_4_a2,
     author = {B. Gonz\'alez Merino},
     title = {Improving {Bounds} for the {Perel'man-Pukhov} {Quotient} for {Inner} and {Outer} {Radii}},
     journal = {Journal of convex analysis},
     pages = {1099--1116},
     year = {2017},
     volume = {24},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_4_JCA_2017_24_4_a2/}
}
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B. González Merino. Improving Bounds for the Perel'man-Pukhov Quotient for Inner and Outer Radii. Journal of convex analysis, Tome 24 (2017) no. 4, pp. 1099-1116. http://geodesic.mathdoc.fr/item/JCA_2017_24_4_JCA_2017_24_4_a2/