A Minkowski-type theorem for covering minima in the plane

For a convex bodyKE² and a latticeLE² let _i(K, L),i=1, 2, denote its covering minima introduced by Kannan and Lovasz. We show ₁(K, L) ₂(K, L)V(K)3/4 det(L), whereV denotes the area. This inequality is tight and there are five different cases of equality.