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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)


Some geometric properties of convex bodies. II

Author: V. V. Makeev
Translated by: N. Yu. Netsvetaev
Original publication: Algebra i Analiz, tom 15 (2003), nomer 6.
Journal: St. Petersburg Math. J. 15 (2004), 867-874
MSC (2000): Primary 52A10, 52A15
Published electronically: November 16, 2004
MathSciNet review: 2044632
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Abstract | References | Similar Articles | Additional Information

Abstract: Topological means are used for the study of approximation of $2$-dimensional sections of a $3$-dimensional convex body by affine-regular pentagons and approximation of a centrally symmetric convex body by a prism. Also, the problem of estimating the relative surface area of the sphere in a normed $3$-space, the problem on universal covers for sets of unit diameter in Euclidean space, and some related questions are considered.

References [Enhancements On Off] (What's this?)

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Additional Information

V. V. Makeev
Affiliation: Universitetskiĭ Pr. 27, St. Petersburg 190000, Russia

PII: S 1061-0022(04)00836-2
Keywords: Convex body, figure, field of convex bodies, relative surface area
Received by editor(s): December 25, 2002
Published electronically: November 16, 2004
Additional Notes: The paper was revised by the author for the English edition.
Article copyright: © Copyright 2004 American Mathematical Society

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