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Minimal requirements for Minkowski's theorem in the plane II
Published online by Cambridge University Press: 17 April 2009
Abstract
Let K be a closed convex set in the Euclidean plane, with area A(K), which contains in its interior only one point 0 of the integer lattice. If K has other than one or three chords through 0 of one of the following types, it is shown that A(K) ≤ 4, while if K has three of one type, A(K) ≤ 4.5. The types of chords considered are chords which partition K into two regions of equal area, chords which lie midway between parallel supporting lines of K, and chords such that K is invariant under reflection in them. The results are generalised to any lattice in the plane.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 22 , Issue 2 , October 1980 , pp. 275 - 283
- Copyright
- Copyright © Australian Mathematical Society 1980
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