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Zapiski Nauchnykh Seminarov POMI, 1998, Volume 252, Pages 165–174
(Mi znsl700)
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This article is cited in 7 scientific papers (total in 7 papers)
Special configurations of planes associated with convex compact
V. V. Makeev Saint-Petersburg State University
Abstract:
Topological methods are applied for proving several combinatorial geometry properties of convex compact sets.
It is proved that if $K_1,\dots,K_{n-1}$ are convex compacta in $\mathbb R^n$, then there is an $(n-2)$-plane $E\subset\mathbb R$ such that for $i=1,2,\dots,n-1$ there exist three (two orthogonal) hyperplanes through $E$ dividing each of $K_i$ into six (four) parts of equal volume. It is also proved that for every two bounded centrally symmetric continuous distributions of masses in $R^3$ with common center of symmetry there are three planes through this center, dividing both masses into eight equal parts.
Received: 13.04.1998
Citation:
V. V. Makeev, “Special configurations of planes associated with convex compact”, Geometry and topology. Part 3, Zap. Nauchn. Sem. POMI, 252, POMI, St. Petersburg, 1998, 165–174; J. Math. Sci. (New York), 104:4 (2001), 1358–1363
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https://www.mathnet.ru/eng/znsl700 https://www.mathnet.ru/eng/znsl/v252/p165
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Abstract page: | 137 | Full-text PDF : | 54 |
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