Geodesic
Estimating the surface area of spheres in normed spaces
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 12, Tome 415 (2013), pp. 21-23 
V. V. Makeev; M. Yu. Nikanorova. Estimating the surface area of spheres in normed spaces. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 12, Tome 415 (2013), pp. 21-23. http://geodesic.mathdoc.fr/item/ZNSL_2013_415_a2/
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     author = {V. V. Makeev and M. Yu. Nikanorova},
     title = {Estimating the surface area of spheres in normed spaces},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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 the paper, it is proved, in particular, that the surface area of the unit sphere in any three-dimensional normed space does not exceed 8.

[1] I. K. Babenko, “Asimptoticheskii ob'ëm torov i geometriya vypuklykh tel”, Mat. zametki, 44:2 (1988), 177–190 | MR | Zbl

[2] V. V. Makeev, “O parallelepipedakh i tsentralno-simmetrichnykh shestiugolnykh prizmakh, opisannykh vokrug trëkhmernogo tsentralno-simmetrichnogo vypuklogo tela”, Zap. nauchn. semin. POMI, 372, 2009, 103–107 | MR