Geodesic
On Benson’s Definition of Area in Minkowski Space
Canadian mathematical bulletin, Tome 42 (1999) no. 2, pp. 237-247

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DOI

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.
DOI : 10.4153/CMB-1999-029-8
Mots-clés : 52A21, 52A38 
Thompson, A. C. On Benson’s Definition of Area in Minkowski Space. Canadian mathematical bulletin, Tome 42 (1999) no. 2, pp. 237-247. doi: 10.4153/CMB-1999-029-8
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     author = {Thompson, A. C.},
     title = {On {Benson{\textquoteright}s} {Definition} of {Area} in {Minkowski} {Space}},
     journal = {Canadian mathematical bulletin},
     pages = {237--247},
     year = {1999},
     volume = {42},
     number = {2},
     doi = {10.4153/CMB-1999-029-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1999-029-8/}
}
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