GEOMETRIC INEQUALITY WITH APPLICATIONS TO LINEAR-FORMS

Let CNbe a cube of volume one centered at the origin in RNand let Pkbe a K-dimensional subspace of ℛN. We prove that CN∩ Pkhas K-dimensionai volume greater than or equal to one. As an application of this inequality we obtain a precise version of Minkowski’s linear forms theorem. We also state a conjecture which would allow our method to be generalized. © 1979 by Pacific Journal of Mathematics.