Mathematika

Research Article

A note on a problem of H. Busemann and C. M. Petty concerning sections of symmetric convex bodies

Apostolos A. Giannopoulosa1

a1 Mathematics Department, University of Crete, Iraklion, Crete, Greece.

Abstract

Let

S002557930001295X_eqnU1

It is proved that for suitable a and b, n≥7, one can have Vn(An) = Vn(Bn) and for every (n–1)-dimensional subspace H of n, where Bn is the unit ball of n. This strengthens previous negative results on a problem of H. Busemann and C. M. Petty.

(Received September 01 1989)

Key Words:

  • 52A20: CONVEX SETS AND RELATED GEOMETRIC TOPICS; Convex sets in n dimensions.