On the Lassak Conjecture for a Convex Body
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 $C \subset R^n$, then $\sum_{i=1}^n \frac{1}{\omega_i} \geq 1$. Here $\omega_i$ denotes the width of $C$ in the direction of the ith coordinate axi...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2011-09-01
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| Series: | Modelirovanie i Analiz Informacionnyh Sistem |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/1059 |
| Summary: | 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 $C \subset R^n$, then $\sum_{i=1}^n \frac{1}{\omega_i} \geq 1$. Here $\omega_i$ denotes the width of $C$ in the direction of the ith 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 $\sum_{i=1}^n \frac{1}{\omega_i} = 1$. |
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| ISSN: | 1818-1015 2313-5417 |