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Minkowski's fundamental inequality for reduced positive quadratic forms(II)
Published online by Cambridge University Press: 09 April 2009
Abstract
A convex polytope D (α) was defined in Barnes (1978) as the set of Minkowski-reduced forms with prescribed diagonal coefficients α1, α2,…αn. A local minimum of the determinant D(f) over D(α) must occur at a vertex of D(α). Here a criterion is obtained for a given vertex to provide a local minimum, completely analogous to Voronoï's criterion for a perfect form to be extreme.
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- Copyright © Australian Mathematical Society 1979
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