Geodesic
Stable lattices and the diagonal group
Journal of the European Mathematical Society, Tome 18 (2016) no. 8, pp. 1753-1767

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DOI

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 
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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     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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