Vol. 85, No. 1, 1979

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ISSN: 0030-8730
n-dimensional area and content in Minkowski spaces

Raymond D. Holmes and Anthony Charles Thompson

Vol. 85 (1979), No. 1, 77–110
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
Authors
Raymond D. Holmes
Anthony Charles Thompson