Minkowski's conjecture for n = 5; a theorem of Skubenko

Abstract

A theorem of Skubenko asserts that if L is a lattice in R5, then there exist positive real numbers λ₁,..., λ₅ such that L has five linearly independent points on the boundary of the ellipsoid Σ⁵ _i=1 λ_ix²_i ≤1 and none other than the origin in its interior. A different proof of this result is given for the case when L has homogeneous minimum different from zero.