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On Benson's Definition of Area in Minkowski Space |
Canad. Math. Bull. 42(1999), 237-247
Published:1999-06-01
Printed: Jun 1999
Printed: Jun 1999
- A. C. Thompson
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] |