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# On Benson's Definition of Area in Minkowski Space

Published:1999-06-01
Printed: Jun 1999
• A. C. Thompson
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## Abstract

Let $(X, \norm)$ 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 \cite{ben1}, \cite{ben2}. In particular, we show that this definition is convex and give details about the nature of the solution to the isoperimetric problem.
 MSC Classifications: 52A21 - Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx] 52A38 - Length, area, volume [See also 26B15, 28A75, 49Q20]

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