The surface area of a polyhedron in a normed space is defined as the sum of the areas of its faces, each divided by the area of the central section of the unit ball, parallel to the face. This functional naturally extends to convex bodies. In this paper, it is proved, in particular, that the surface area of the unit sphere in any three-dimensional normed space does not exceed 8.
|Number of pages||2|
|Journal||Journal of Mathematical Sciences|
|Early online date||11 Jan 2016|
|Publication status||Published - 2016|