期刊论文详细信息
Modelirovanie i Analiz Informacionnyh Sistem | |
On the Lassak Conjecture for a Convex Body | |
M. V. Nevskii1  | |
[1] Ярославский государственный университет им. П.Г. Демидова; | |
关键词: convex body; width; axial diameter; homothety; simplex; interpolation; projection; | |
DOI : | |
来源: DOAJ |
【 摘 要 】
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 $\sum_{i=1}^n \frac{1}{\omega_i} = 1$.
【 授权许可】
Unknown