Contact points of convex bodies (Q1380499)

The author proves that given some positive \(\varepsilon\) and \(n\)-dimensional convex body, there is another convex body having \(m\) contact points whose Banach-Mazur distance from \(B\) is at most \(\varepsilon +1 \) with \(m\leq C(\varepsilon)n\log^3{n}\). The author announces a similar theorem with the first power of \(\log n\) whose proof will appear elsewhere.