@article{02ac348d8eed4f779f90c98500b9e779,
title = "The minimal length product over homology bases of manifolds",
abstract = "Minkowski{\textquoteright}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.",
author = "Florent Balacheff and Steve Karam and Hugo Parlier",
note = "Funding Information: Florent Balacheff acknowledges support from the European Social Fund and the Agencia Estatal de Investigaci{\'o}n through the Ram{\'o}n y Cajal grant RYC-2016-19334 “Local and global systolic geometry and topology”, as well as from the grant ANR-12-BS01-0009-02. Steve Karam acknowledges support from grant ANR CEMPI (ANR-11-LABX-0007-01). Hugo Parlier acknowledges support from the ANR/FNR project SoS, INTER/ANR/16/11554412/SoS, ANR-17-CE40-0033. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.",
year = "2021",
month = jun,
doi = "10.1007/s00208-021-02150-5",
language = "English",
volume = "380",
pages = "825--854",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer New York",
number = "1-2",
}