Exponential lower bound for the translative kissing numbers of \(d\)-dimensional convex bodies (Q1387856)

The translate kissing number or Hadwiger number \(H(K)\) of a convex body \(K\) of \(\mathbb{R}^d\) is the maximum number of mutually nonoverlapping translates of \(K\) which touch \(K\). The author shows that \(H(K) \geq 2^{cd}\) for all \(K\subset \mathbb{R}^d\) with an absolute constant \(c>0\).