On Young hulls of convex curves in R^{2n}

Abstract

For a convex curve in an even-dimensional affine space we introduce a series of convex domains (called Young hulls), describe their structure and give a formulas fo the volume of the biggest of these domains. This paper is an attempt to generalize the classical isoperimetric inequality for the volume of the convex hull of a space curve due to I.Schoenberg.