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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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 |
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doaj-bd2dfb83499d4b43a4d225b38424805b2021-07-29T08:15:17ZengYaroslavl State UniversityModelirovanie i Analiz Informacionnyh Sistem1818-10152313-54172011-09-01183511800On the Lassak Conjecture for a Convex BodyM. V. Nevskii0Ярославский государственный университет им. П.Г. ДемидоваIn 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 $\sum_{i=1}^n \frac{1}{\omega_i} = 1$.https://www.mais-journal.ru/jour/article/view/1059convex bodywidthaxial diameterhomothetysimplexinterpolationprojection |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. V. Nevskii |
| spellingShingle |
M. V. Nevskii On the Lassak Conjecture for a Convex Body Modelirovanie i Analiz Informacionnyh Sistem convex body width axial diameter homothety simplex interpolation projection |
| author_facet |
M. V. Nevskii |
| author_sort |
M. V. Nevskii |
| title |
On the Lassak Conjecture for a Convex Body |
| title_short |
On the Lassak Conjecture for a Convex Body |
| title_full |
On the Lassak Conjecture for a Convex Body |
| title_fullStr |
On the Lassak Conjecture for a Convex Body |
| title_full_unstemmed |
On the Lassak Conjecture for a Convex Body |
| title_sort |
on the lassak conjecture for a convex body |
| publisher |
Yaroslavl State University |
| series |
Modelirovanie i Analiz Informacionnyh Sistem |
| issn |
1818-1015 2313-5417 |
| publishDate |
2011-09-01 |
| description |
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 $\sum_{i=1}^n \frac{1}{\omega_i} = 1$. |
| topic |
convex body width axial diameter homothety simplex interpolation projection |
| url |
https://www.mais-journal.ru/jour/article/view/1059 |
| work_keys_str_mv |
AT mvnevskii onthelassakconjectureforaconvexbody |
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1721256609263386624 |