Small separators, upper bounds for $l^{\infty }$-widths, and systolic geometry

Sergey Avvakumov, Alexander Nabutovsky

We investigate the dependence on the dimension in the inequalities that relate the Euclidean volume of a closed submanifold $M^n\subset {\mathbb{R}}^N$ with its $l^{\infty }$-width $W^{…