Vol. 83, No. 2, 1979

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
A geometric inequality with applications to linear forms

Jeffrey D. Vaaler

Vol. 83 (1979), No. 2, 543–553

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
Received: 21 November 1978
Revised: 19 February 1979
Published: 1 August 1979
Jeffrey D. Vaaler
Department of Mathematics
University of Texas at Austin
1 University Station - C1200
Austin TX 78712-0257
United States