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Model. Anal. Inform. Sist., 2011, Volume 18, Number 3, Pages 5–11 (Mi mais181)  

This article is cited in 1 scientific paper (total in 1 paper)

On the Lassak conjecture for a convex body

M. V. Nevskii

P. G. Demidov Yaroslavl State University

Abstract: In 1993 M. Lassak formulated (in the equivalent form) the following conjecture. If we can inscribe a translate of the cube $[0,1]^n$ into a convex body $C\subset\mathbb R^n$, then $\sum_{i=1}^n 1/w_i\geq 1$. Here $w_i$ denotes the width of $C$ in the direction of the $i$th coordinate axis. The paper contains a new proof of this statement for $n=2$. Also we show that if a translate of $[0,1]^n$ can be inscribed into the $n$-dimensional simplex, then for this simplex holds $\sum_{i=1}^n 1/w_i= 1$.

Keywords: convex body, width, axial diameter, homothety, simplex, interpolation, projection.

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UDC: 514.17+517.51
Received: 23.05.2011

Citation: M. V. Nevskii, “On the Lassak conjecture for a convex body”, Model. Anal. Inform. Sist., 18:3 (2011), 5–11

Citation in format AMSBIB
\Bibitem{Nev11}
\by M.~V.~Nevskii
\paper On the Lassak conjecture for a convex body
\jour Model. Anal. Inform. Sist.
\yr 2011
\vol 18
\issue 3
\pages 5--11
\mathnet{http://mi.mathnet.ru/mais181}


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    This publication is cited in the following articles:
    1. M. V. Nevskii, “O nekotorykh rezultatakh po geometrii vypuklykh tel i ikh prilozheniyakh”, Model. i analiz inform. sistem, 19:3 (2012), 113–123  mathnet
  • Моделирование и анализ информационных систем
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