TY - JOUR

T1 - Estimating the Surface Area of Spheres in Normed Spaces

AU - Makeev, V. V.

AU - Nikanorova, M. Yu.

N1 - Makeev, V.V., Nikanorova, M.Y. Estimating the Surface Area of Spheres in Normed Spaces. J Math Sci 212, 531–532 (2016). https://doi.org/10.1007/s10958-016-2681-9

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Russia

KW - Hexagonal

KW - Small Area

KW - Small Volume

KW - Unit Ball

UR - https://link.springer.com/article/10.1007/s10958-016-2681-9

M3 - Article

VL - 212

SP - 531

EP - 532

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -