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International Conference on Algebra, Analysis and Geometry - 2021
August 23, 2021 15:05, Kazan, Kazan Federal University
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On the Brunn and Brunn–Minkowski theorems
F. M. Malyshev |
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Abstract:
The case of equality in the Brunn-Minkowski theorem presents the greatest difficulty for the reason
that so far the proofs have been carried out not for three parallel sections of convex bodies, as in
Brunn's, but for Minkowski sums. The cuts used by Brunn are sufficient for an elementary (accessible
to schoolchildren) proof of the theorem. Scribe the case of equality to Minkowski.
Keywords: convex bodies, polyhedra, Brunn-Minkowski inequality.
Supplementary materials:
abstract.pdf (248.4 Kb)
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