Improved packing of hypersurfaces in ${\mathbb{R}}^d$

Xianghong Chen, Tongou Yang, Yue Zhong

For $d\ge 1$, we construct a compact subset $K\subseteq {\mathbb{R}}^{d+1}$ containing a $d$-sphere of every radius between $1$ and $2$, such that for every $\hat{I}´\in (0,1)$, the $\hat{I}´$-…