A geometric inequality with applications to linear forms

Jeffrey D. Vaaler

Vol. 83 (1979), No. 2, 543–553

DOI: 10.2140/pjm.1979.83.543

Abstract

Let C_N be a cube of volume one centered at the origin in R^N and let P_K be a K-dimensional subspace of R^N. We prove that C_N ∩P_K has K-dimensional 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.

Mathematical Subject Classification 2000

Primary: 52A40

Secondary: 10E15

Milestones

Received: 21 November 1978

Revised: 19 February 1979

Published: 1 August 1979