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- W2897062394 abstract "Minkowski's second theorem can be stated as an inequality for $n$-dimensional flat Finsler tori relating the volume and the minimal product of the lengths of closed geodesics which form a homology basis. In this paper we show how this fundamental result can be promoted to a principle holding for a larger class of Finsler manifolds. This includes manifolds for which first Betti number and dimension do no necessarily coincide, a prime example being the case of surfaces. This class of manifolds is described by a non-vanishing condition for the hyperdeterminant reduced modulo $2$ of the multilinear map induced by the fundamental class of the manifold on its first ${mathbb Z}_2$-cohomology group using the cup product." @default.
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- W2897062394 date "2018-10-18" @default.
- W2897062394 modified "2023-09-27" @default.
- W2897062394 title "Minimal length product over homology bases of manifolds" @default.
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