Estimates of the asphericity of sections of convex bodies

We define the function (n, k) to be the infimum of all such that any bounded centrally symmetric convex body inRⁿ possesses an -asphericalk-dimensional central section. It is proved that (3, 2)=2–1 and (n, n-1)n-1-1. Several related functions are defined and their values on the pairs (n, n-1) are estimated.Translated from Ukrainskií Geometricheskií Sbornik, Issue 28, 1985, pp. 76–79.