The inner aperture of a convex set

Arne Brøndsted

Vol. 72 (1977), No. 2, 335–340

DOI: 10.2140/pjm.1977.72.335

Abstract

It is a standard fact that the asymptotic cone O(C) of a convex set C in Rⁿ is the polar of the barrier cone B(C). In the present note we show that the inner aperture P(C) of C may be obtained from B(C) in a similar manner. We use this result to study relations between O(C) and P(C), and to give a short proof of D. G. Larman’s characterization of inner apertures.

Mathematical Subject Classification 2000

Primary: 52A20

Milestones

Received: 14 December 1976

Revised: 14 April 1977

Published: 1 October 1977