The minimal length product over homology bases of manifolds
Balacheff, Florent Nicolas (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Karam, Steve (Lebanese University)
Parlier, Hugo (University of Luxembourg. Department of Mathematics)

Data:	2021
Resum:	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 Z2-cohomology group using the cup product.
Ajuts:	Ministerio de Economía, Industria y Competitividad RYC-2016-19334
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Publicat a:	Mathematische Annalen, Vol. 380, Issue 1-2 (June 2021) , p. 825-854, ISSN 1432-1807

DOI: 10.1007/s00208-021-02150-5

Postprint 25 p, 464.2 KB

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