n-dimensional area and content in Minkowski spaces

Raymond D. Holmes and Anthony Charles Thompson

Vol. 85 (1979), No. 1, 77–110

DOI: 10.2140/pjm.1979.85.77

Abstract

A definition of content in Minkowski spaces (of any finite dimension) is given which implies that the surface of the unit ball and that of the dual ball are equal. Various consequences of this definition, including the solution to the isoperimetric problem, are explored. Numerous examples and some unsolved problems are given in the last two sections.

Mathematical Subject Classification 2000

Primary: 52A40

Milestones

Received: 13 January 1977

Revised: 1 November 1977

Published: 1 November 1979