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On Benson’s Definition of Area in Minkowski Space

Published online by Cambridge University Press:  20 November 2018

A. C. Thompson
A. C. Thompson*
Affiliation:
Department of Mathematics, Statistics and Computing Science Dalhousie University Halifax, Nova Scotia B3H 3J5
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Abstract

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Let $(X,\,\left\| \,.\, \right\|)$ be a Minkowski space (finite dimensional Banach space) with unit ball $B$. Various definitions of surface area are possible in $X$. Here we explore the one given by Benson [1], [2]. In particular, we show that this definition is convex and give details about the nature of the solution to the isoperimetric problem.

Keywords

52A2152A38
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 2 , 01 June 1999 , pp. 237 - 247
Copyright
Copyright © Canadian Mathematical Society 1999

References

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