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A new extension of Minkowski's Theorem

Published online by Cambridge University Press:  17 April 2009

P.R. Scott
P.R. Scott
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide, South Australia.
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Abstract

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Let K be a closed convex set in the plane containing no nonzero point of the integral lattice. We show that if the area A(K) of K is equally distributed amongst the four principal quadrants of the plane, then A(K) < 4.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 3 , June 1978 , pp. 403 - 405
Copyright
Copyright © Australian Mathematical Society 1978

References

[1]Scott, P.R., “An analogue of Minkowski's theorem in the plane”, J. London Math. Soc. (2) 8 (1974), 647–651.CrossRefGoogle Scholar