On finite lattice coverings (Q1601381)

The authors investigate optimal finite lattice coverings of strictly convex bodies with respect to the parametric density. They prove that the optimal arrangement in the plane is either a sausage, a so-called double sausage or tends to a Wulff-shape, depending on the parameter. In arbitrary dimension they give a characterization of lattices for which the optimal finite lattice covering with the unit ball is a sausage, for large parameter.