I guess the formulation of the Minkowski-Hlawka theorem should be strongly generalized from balls to central symmetric convex bodies. Cf. section 3.1 in "Sphere packings", Chuanming Zong,John Talbot. See http://www.amazon.com/Sphere-Packings-Universitext-Chuanming-Zong/dp/0387987940/ resp. google books on page 47. Shuber2 (talk) 10:54, 13 December 2009 (UTC)
In the introduction of Siegel, 1944, "A mean value theorem in geometry of numbers" one can read: "As a consequence Hlawka deduced an assertion of Minkowski which had remained unproven for more than fifty years: 'If B is an n-dimensional star domain of volume < zeta(n), then there exists a lattice of determinant 1 such that B does not contain any lattice point != 0.'
Hence, the formulation should even be extended to star-shaped sets, which includes balls as an extremely special case. However, I have also another concern on the current formulation on the theorem. In Gruber, "Convex and Discrete Geometry" the formulation is as follows: 'Let J be a Jordan measurable set in E^d with V(J) < 1. Then there is a lattice L in Ed with d(L) = 1 which contains no point of J, with the possible exception of o.'