On the Lassak Conjecture for a Convex Body

Modelirovanie i Analiz Informacionnyh Sistem

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