Uri Shapira, Barak Weiss
Published 2016-09-27Version 1
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 behaviour 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.
Comments: This paper was part of the paper "On stable lattices and the diagonal group" (arXiv:1309.4025) which was split into three shorter papers (now all on arXiv) following the referee's request
Journal: Journal of the European Mathematical Society. Volume 18, Issue 8, 2016, pp. 1753 - 1767
Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions
Asymptotic behaviour of measure for captured trajectories into parametric autoresonance
Limiting distribution of translates of a closed orbit of diagonal group on $SL(n,\mathbb{R})/SL(n,\mathbb{Z})$
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