Successive minima, intrinsic volumes, and lattice determinants
For arbitrary lattices in euclidean \(d\)-space \(E^ d\) the author considers inequalities between the successive minima \(\lambda_ i\) and the intrinsic volumes \(V_ i\) of \(O\)-symmetric convex bodies, i.e. analogues of Minkowski's second fundamental theorem in Geometry of Numbers. Clearly the \(V_ i\) (except the volume) are not equi-affine invariant, so suitable functionals of the lattice have to be introduced, which lead to a general series of inequalities between the \(\lambda_ i\), the \(V_ i\) and suitable lattice constants.
scientific article; zbMATH DE number 735347
scientific article