Vol. 83, No. 2, 1979

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A geometric inequality with applications to linear forms

Jeffrey D. Vaaler

Vol. 83 (1979), No. 2, 543–553
Abstract

Let CN be a cube of volume one centered at the origin in RN and let PK be a K-dimensional subspace of RN. We prove that CN PK 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
Authors
Jeffrey D. Vaaler
Department of Mathematics
University of Texas at Austin
1 University Station - C1200
Austin TX 78712-0257
United States