Geodesic
Stable lattices and the diagonal group
Journal of the European Mathematical Society, Tome 18 (2016) no. 8, pp. 1753-1767 Cet article a éte moissonné depuis la source EMS Press

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Inspired by work of McMullen, we show that any orbit of the diagonal group in the space of lattices accumulates on the set of stable lattices. As consequences, we settle a conjecture of Ramharter concerning the asymptotic behavior of the Mordell constant, and reduce Minkowski’s conjecture on products of linear forms to a geometric question, yielding two new proofs of the conjecture in dimensions up to 7.
DOI : 10.4171/jems/628
Classification : 37-XX, 11-XX
Keywords: Lattices, stable, diagonal group 
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     author = {Uri Shapira and Barak Weiss},
     title = {Stable lattices and the diagonal group},
     journal = {Journal of the European Mathematical Society},
     pages = {1753--1767},
     year = {2016},
     volume = {18},
     number = {8},
     doi = {10.4171/jems/628},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/628/}
}
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Uri Shapira; Barak Weiss. Stable lattices and the diagonal group. Journal of the European Mathematical Society, Tome 18 (2016) no. 8, pp. 1753-1767. doi: 10.4171/jems/628

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