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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 415, Pages 21–23 (Mi znsl5681)  
Estimating the surface area of spheres in normed spaces

V. V. Makeev, M. Yu. Nikanorova

St. Petersburg State University, St. Petersburg, Russia
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Abstract: 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.
Key words and phrases: surface area in a normed space, convex body, parallelepiped.
Received: 31.12.2012
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 212, Issue 5, Pages 531–532
DOI: https://doi.org/10.1007/s10958-016-2681-9
Bibliographic databases:
Document Type: Article
UDC: 514.172
Language: Russian
Citation: V. V. Makeev, M. Yu. Nikanorova, “Estimating the surface area of spheres in normed spaces”, Geometry and topology. Part 12, Zap. Nauchn. Sem. POMI, 415, POMI, St. Petersburg, 2013, 21–23; J. Math. Sci. (N. Y.), 212:5 (2016), 531–532
Citation in format AMSBIB
\Bibitem{MakNik13}
\by V.~V.~Makeev, M.~Yu.~Nikanorova
\paper Estimating the surface area of spheres in normed spaces
\inbook Geometry and topology. Part~12
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 415
\pages 21--23
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5681}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 212
\issue 5
\pages 531--532
\crossref{https://doi.org/10.1007/s10958-016-2681-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84959098291}
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